By the end of this chapter, you should be able to:
Define and explain the function of each macronutrient and type of micronutrient.
Examine factors that affect the quality of food.
Discuss influences on food choice.
Outline how to achieve a healthy diet.
Describe programs that support nutrition in early care and education programs.
Identify ways to assess the quality of meals and snacks in early care and education programs.
WI Department of Children and Familities Licensing Rules for Group Child Care Centers
DCF 251 Administrative Code regulations that relate to this chapter include:
FOOD SERVICE
251.06(9)(c)3m: Meals shall be prepared on the premises, in a central kitchen operated by the child care center or in another location that has been inspected by a representative of a state agency.
Licensed child care providers must
Follow the Federal Child and Adult Care Food Program (CACFP) meal plan requirements.
Participate in the orientation under s. DCF 251.05 (4) (a) and shall document annual training of at least 4 hours in kitchen sanitation, food handling, and nutrition.
Introduction
In order to plan, prepare, and serve nutritious foods to children in early care and education programs it’s important to have a basic understanding of nutrition and the programs and resources available to support meeting children’s nutrition needs.
What are Nutrients?
The foods we eat contain nutrients. Nutrients are substances required by the body to perform its basic functions. Nutrients must be obtained from our diet, since the human body does not synthesize or produce them. Nutrients have one or more of three basic functions: they provide energy, contribute to body structure, and/or regulate chemical processes in the body. These basic functions allow us to detect and respond to environmental surroundings, move, excrete wastes, respire (breathe), grow, and reproduce. There are six classes of nutrients required for the body to function and maintain overall health. These are carbohydrates, fats, proteins, water, vitamins, and minerals. Foods also contain non-nutrients that may be harmful (such as natural toxins common in plant foods and additives like some dyes and preservatives) or beneficial (such as antioxidants).
Macronutrients
Nutrients that are needed in large amounts are called macronutrients. There are three classes of macronutrients: carbohydrates, fats, and proteins. These can be metabolically processed into cellular energy, allowing our bodies to conduct their basic functions. A unit of measurement of food energy is the calorie. Water is also a macronutrient in the sense that you require a large amount of it, but unlike the other macronutrients, it does not yield calories.
Carbohydrates
Carbohydrates are molecules composed of carbon, hydrogen, and oxygen. The major food sources of carbohydrates are grains, milk, fruits, and starchy vegetables, like potatoes. Non-starchy vegetables also contain carbohydrates, but in lesser quantities. Carbohydrates are broadly classified into two forms based on their chemical structure: simple carbohydrates, often called simple sugars; and complex carbohydrates.
Simple carbohydrates consist of one or two basic units. Examples of simple sugars include sucrose, the type of sugar you would have in a bowl on the breakfast table, and glucose, the type of sugar that circulates in your blood.
Complex carbohydrates are long chains of simple. During digestion, the body breaks down digestible complex carbohydrates to simple sugars, mostly glucose. Glucose is then transported to all our cells where it is stored, used to make energy, or used to build macromolecules. Fiber is also a complex carbohydrate, but it cannot be broken down by digestive enzymes in the human intestine. As a result, it passes through the digestive tract undigested unless the bacteria that inhabit the colon or large intestine break it down.
One gram of digestible carbohydrates yields four kilocalories of energy for the cells in the body to perform work. In addition to providing energy and serving as building blocks for bigger macromolecules, carbohydrates are essential for proper functioning of the nervous system, heart, and kidneys. As mentioned, glucose can be stored in the body for future use.
Fats
Fat (officially called lipids) are also a family of molecules composed of carbon, hydrogen, and oxygen, but unlike carbohydrates, they are insoluble in water. Fats are found predominantly in butter, oils, meats, dairy products, nuts, and seeds, and in many processed foods. The main job of fats is to provide or store energy. Fats provide more energy per gram than carbohydrates (nine kilocalories per gram of fats versus four kilocalories per gram of carbohydrates). In addition to energy storage, fats serve as a major component of cell membranes, surround and protect organs (in fat-storing tissues), provide insulation to aid in temperature regulation, and regulate many other functions in the body.
Proteins
Proteins are macromolecules composed of chains of subunits called amino acids. Amino acids are simple subunits composed of carbon, oxygen, hydrogen, and nitrogen. Food sources of proteins include meats, dairy products, seafood, and a variety of different plant-based foods, most notably soy. The word protein comes from a Greek word meaning “of primary importance,” which is an apt description of these macronutrients; they are also known colloquially as the “workhorses” of life. Proteins provide four kilocalories of energy per gram; however providing energy is not protein’s most important function. Proteins provide structure to bones, muscles and skin, and play a role in conducting most of the chemical reactions that take place in the body. Scientists estimate that more than one-hundred thousand different proteins exist within the human body. The genetic codes in DNA are basically protein recipes that determine the order in which 20 different amino acids are bound together to make thousands of specific proteins.
Water
There is one other nutrient that we must have in large quantities: water. Water does not contain carbon, but is composed of two hydrogens and one oxygen per molecule of water. More than 60 percent of your total body weight is water. Without it, nothing could be transported in or out of the body, chemical reactions would not occur, organs would not be cushioned, and body temperature would fluctuate widely.
Protein
Carbohydrates
Fats
Water
Figure 12.1 – The Macronutrients: Carbohydrates, Fats, Protein, and
Water
545
Micronutrients
Micronutrients are nutrients required by the body in lesser amounts, but are still essential for carrying out bodily functions. Micronutrients include all the essential minerals and vitamins. There are sixteen essential minerals and thirteen vitamins (See Table 12.1 “Minerals and Their Major Functions” and Table 12.2 “Vitamins and Their Major Functions” for a complete list and their major functions). In contrast to carbohydrates, fats, and proteins, micronutrients are not sources of energy (calories), but they assist in the process as components of enzymes. Enzymes are proteins that cause chemical reactions in the body and are involved in all aspects of body functions from producing energy, to digesting nutrients, to building macromolecules. Micronutrients play many essential roles in the body.
Minerals
Minerals are solid inorganic substances that form crystals and are classified depending on how much of them we need. Trace minerals, such as molybdenum, selenium, zinc, iron, and iodine, are only required in a few milligrams or less. Macrominerals, such as calcium, magnesium, potassium, sodium, and phosphorus, are required in hundreds of milligrams. Many minerals are critical for enzyme function, others are used to maintain fluid balance, build bone tissue, synthesize hormones, transmit nerve impulses, contract and relax muscles, and protect against harmful free radicals in the body that can cause health problems such as cancer.
Table 12.1 – Minerals and Their Major
Functions
546
Bone and teeth health maintenance, nerve transmission, muscle contraction, blood clotting
Phosphorus
Bone and teeth health maintenance, acid-base balance
Magnesium
Protein production, nerve transmission, muscle contraction
Sulfur
Protein production
Trace Minerals
Mineral
Major Function
Iron
Carries oxygen, assists in energy production
Zinc
Protein and DNA production, wound healing, growth, immune system function
Iodine
Thyroid hormone production, growth, metabolism
Selenium
Antioxidant
Copper
Coenzyme, iron metabolism
Manganese
Coenzyme
Fluoride
Bone and teeth health maintenance, tooth decay prevention
Chromium
Assists insulin in glucose metabolism
Molybdenum
Coenzyme
Vitamins
The thirteen vitamins are categorized as either water-soluble or fat-soluble. The water-soluble vitamins are vitamin C and all the B vitamins, which include thiamine, riboflavin, niacin, pantothenic acid, pyridoxine, biotin, folate and cobalamin. Unneeded water soluble vitamins are excreted from the body. The fat-soluble vitamins are A, D, E, and K. Vitamins are required to perform many functions in the body such as making red blood cells, synthesizing bone tissue, and playing a role in normal vision, nervous system function, and immune system function. Fat soluble vitamins are stored in the body in fat (and can become toxic when too much is consumed, almost always from supplements).
Table 12.2 – Vitamins and Their Major
Functions
547
Water Soluble
Vitamin
Major Function
Thiamin (B1)
Coenzyme, energy metabolism assistance
Riboflavin (B2 )
Coenzyme, energy metabolism assistance
Niacin (B3)
Coenzyme, energy metabolism assistance
Pantothenic acid (B5)
Coenzyme, energy metabolism assistance
Pyridoxine (B6)
Coenzyme, amino acid synthesis assistance
Biotin (B7)
Coenzyme, amino acid and fatty acid metabolism
Folate (B9)
Coenzyme, essential for growth
Cobalamin (B12)
Coenzyme, red blood cell synthesis
C (ascorbic acid)
Collagen synthesis, antioxidant
Fat Soluble
Vitamin
Major Function
A
Vision, reproduction, immune system function
D
Bone and teeth health maintenance, immune system function
E
Antioxidant, cell membrane protection
K
Bone and teeth health maintenance, blood clotting
Vitamin deficiencies can cause severe health problems and even death. Some vitamins have been found to prevent certain disorders and diseases such as scurvy (vitamin C), night blindness (vitamin A), and rickets (vitamin D).
548
Table 12.3 –
Summary of the Functions of
Nutrients
549
Name of Stage
Description of Stage
Protein
Necessary for tissue formation, cell reparation, and hormone and enzyme production. It is essential for building strong muscles and a healthy immune system.
Carbohydrates
Provide a ready source of energy for the body and provide structural constituents for the formation of cells.
Fat
Provides stored energy for the body, functions as structural components of cells and also as signaling molecules for proper cellular communication. It provides insulation to vital organs and works to maintain body temperature.
Vitamins
Regulate body processes and promote normal body-system functions.
Minerals
Regulate body processes, are necessary for proper cellular function, and comprise body tissue.
Water
Transports essential nutrients to all body parts, transports waste products for disposal, and aids with body temperature maintenance.
Quality of Food
One measurement of food quality is the amount of nutrients it contains relative to the amount of energy it provides. High-quality foods are nutrient dense, meaning they contain significant amounts of one or more essential nutrients relative to the amount of calories they provide. Nutrient-dense foods are the opposite of “empty-calorie” foods such as carbonated sugary soft drinks, which provide many calories and very little, if any, other nutrients. Food quality is additionally associated with its taste, texture, appearance, microbial content, and how much consumers like it.
550
Note
Food: A Better Source of Nutrients
It is better to get all your micronutrients from the foods you eat as opposed to from supplements. Supplements contain only what is listed on the label, but foods contain many more macronutrients, micronutrients, and other chemicals, like antioxidants, that benefit health. While vitamins, multivitamins, and supplements are a $20 billion industry in the United States, and more than 50 percent of Americans purchase and use them daily, there is no consistent evidence that they are better than food in promoting health and preventing disease.
551
Food Additives
People have been using food additives for thousands of years. Today more than 3000 substances are used as food additives. Salt, sugar, and corn syrup are by far the most widely used additives in food in this country.
How this might affect the quality (including nutritional value) of food will depend on the additive.
Figure 12.2 – Food Additives
Salt
552
Sugar
553
Food coloring
554
"Food additive" is defined by the Food and Drug Administration (FDA) as any substance that—directly or indirectly—becomes a component or otherwise affects the characteristics of any food. This definition includes any substance used in the production, processing, treatment, packaging, transportation or storage of food.
Additives are used to maintain or improve safety, freshness, nutritional value, taste, texture and appearance. The use of food additives has become more prominent in recent years due to the increased production of prepared, processed, and convenience foods.
According to the FDA, “Direct food additives are those that are added to a food for a specific purpose in that food.” For example, using phosphates in meat and poultry products to retain moisture and protect the flavor.
“Indirect food additives are those that become part of the food in trace amounts due to its packaging, storage or other handling,” according to the FDA
.
For instance, minute amounts of packaging substances may find their way into foods during storage. Food packaging manufacturers must prove to the FDA that all materials coming in contact with food are safe before they are permitted for use in such a manner.
FDA defines a color additive as any dye, pigment, or substance which—when added or applied to a food, drug, or cosmetic, or to the human body—is capable (alone or through reactions with other substances) of imparting color. FDA is responsible for regulating all color additives to ensure that foods containing color additives are safe to eat, contain only approved ingredients, and are accurately labeled.
Color additives are used in foods for many reasons: 1) to offset color loss due to exposure to light, air, temperature extremes, moisture, and storage conditions; 2) to correct natural variations in color; 3) to enhance colors that occur naturally; and 4) to provide color to colorless and "fun" foods. Without color additives, colas wouldn't be brown, margarine wouldn't be yellow, and mint ice cream wouldn't be green. Color additives are now recognized as an important part of practically all processed foods we eat.
Today, food and color additives are more strictly studied, regulated, and monitored than at any other time in history. FDA has the primary legal responsibility for determining their safe use. To market a new food or color additive (or before using an additive already approved for one use in another manner not yet approved), a manufacturer or other sponsor must first petition FDA for its approval. These petitions must provide evidence that the substance is safe for the ways in which it will be used.
Before any substance can be added to food, its safety must be assessed in a stringent approval process. The Food Safety and Inspection Service (FSIS) of the U.S. Department of Agriculture (USDA) shares responsibility with FDA for the safety of food additives used in meat, poultry, and egg products. All additives are initially evaluated for safety by FDA.
When an additive is proposed for use in a meat, poultry, or egg product, its safety, technical function, and conditions of use must also be evaluated by the Risk, Innovations and Management Staff of FSIS, as provided in the Federal Meat Inspection Act, the Poultry Products Inspection Act, the Egg Products Inspection Act, and related regulations.
Although FDA has overriding authority regarding additive safety, FSIS may apply even stricter standards that take into account the unique characteristics of meat, poultry, and egg products. Several years ago, for instance, permission was sought to use sorbic acid in meat salads. Although sorbic acid was an approved food additive, permission for use in meat salad was denied because such usage could mask spoilage caused by organisms that cause foodborne illness.
Additives are never given permanent approval. FDA and FSIS continually review the safety of approved additives, based on the best scientific knowledge, to determine if approvals should be modified or withdrawn.
The statutes and regulations to enforce the statutes require certain information on labels of meat and poultry products so consumers will have complete information about a product. In all cases, ingredients must be listed on the product label in the ingredients statement in order by weight, from the greatest amount to the least.
Substances such as spices and spice extractives may be declared as "natural flavors," "flavors," or "natural flavoring" on meat and poultry labels without naming each one. This is because they are used primarily for their flavor contribution and not their nutritional contribution.
Substances such as dried meat, poultry stock, meat extracts, or hydrolyzed protein must be listed on the label by their common or usual name because their primary purpose is not flavor. They may be used as flavor enhancers, binders, or emulsifiers. They must be labeled using the species of origin of the additive, for example, dried beef, chicken stock, pork extract, or hydrolyzed wheat protein.
Color additives must be declared by their common or usual names on labels (for example, FD&C Yellow 5 or annatto extract), not collectively as colorings. These labeling requirements help consumers make choices about the foods they eat.
555
Artificial Sweeteners
Artificial sweeteners, also called sugar substitutes, are substances that are used instead of sucrose (table sugar) to sweeten foods and beverages. Because artificial sweeteners are many times sweeter than table sugar, much smaller amounts (200 to 20,000 times less) are needed to create the same level of sweetness.
Artificial sweeteners are regulated by the U.S. Food and Drug Administration (FDA). Approved artificial sweeteners include:
Aspartame, distributed under several trade names (e.g., NutraSweet
®
and Equal
®
),
Sucralose, marketed under the trade name Splenda
®
Acesulfame potassium (also known as ACK, Sweet One
®
, and Sunett
®
)
Neotame, which is similar to aspartame
Advantame, which is also similar to aspartame
Questions about artificial sweeteners and cancer arose when early studies showed that cyclamate in combination with saccharin caused bladder cancer in laboratory animals. However, results from subsequent carcinogenicity studies (studies that examine whether a substance can cause cancer) of these sweeteners have not provided clear evidence of an association with cancer in humans. Similarly, studies of other FDA-approved sweeteners have not demonstrated clear evidence of an association with cancer in humans.
557
There are other factors besides environment and lifestyle that influence the foods you choose to eat. Different foods affect energy level, mood, how much is eaten, how long before you eat again, and if cravings are satisfied. We have talked about some of the physical effects of food on your body, but there are other effects too.
Food regulates your appetite and how you feel. Multiple studies have demonstrated that some high fiber foods and high-protein foods decrease appetite by slowing the digestive process and prolonging the feeling of being full or satiety. The effects of individual foods and nutrients on mood are not backed by consistent scientific evidence, but in general, most studies support that healthier diets are associated with a decrease in depression and improved well-being. To date, science has not been able to track the exact path in the brain that occurs in response to eating a particular food, but it is quite clear that foods, in general, stimulate emotional responses in people.
Food also has psychological, cultural, and religious significance, so your personal choices of food affect your mind, as well as your body. The social implications of food have a great deal to do with what people eat, as well as how and when. Special events in individual lives—from birthdays to funerals—are commemorated with equally special foods. Being aware of these forces can help people make healthier food choices—and still honor the traditions and ties they hold dear.
Typically, eating kosher food means a person is Jewish; eating fish on Fridays during Lent means a person is Catholic; fasting during the ninth month of the Islamic calendar means a person is Muslim. On New Year’s Day, Japanese take part in an annual tradition of Mochitsuki also known as Mochi pounding in hopes of gaining good fortune over the coming year. Several hundred miles away in Hawai‘i, people eat poi made from pounded taro root with great significance in the Hawaiian culture, as it represents Hāloa, the ancestor of chiefs and kanaka maoli (Native Hawaiians). National food traditions are carried to other countries when people immigrate.
Factors that Drive Food Choices
Along with these influences, a number of other factors affect the dietary choices individuals make, including:
Taste, texture, and appearance. Individuals have a wide range of tastes which influence their food choices, leading some to dislike milk and others to hate raw vegetables. Some foods that are very healthy, such as tofu, may be unappealing at first to many people. However, creative cooks can adapt healthy foods to meet most people’s taste.
Economics. Access to fresh fruits and vegetables may be scant, particularly for those who live in economically disadvantaged or remote areas, where cheaper food options are limited to convenience stores and fast food.
Early food experiences. People who were not exposed to different foods as children, or who were forced to swallow every last bite of overcooked vegetables, may make limited food choices as adults.
Habits. It’s common to establish eating routines, which can work both for and against optimal health. Habitually grabbing a fast food sandwich for breakfast can seem convenient, but might not offer substantial nutrition. Yet getting in the habit of drinking an ample amount of
water
each day can yield multiple benefits.
Culture. The culture in which one grows up affects how one sees food in daily life and on special occasions.
Geography. Where a person lives influences food choices. For instance, people who live in Midwestern US states have less access to seafood than those living along the coasts.
Advertising. The media greatly influences food choice by persuading consumers to eat certain foods.
Social factors. Any school lunchroom observer can testify to the impact of peer pressure on eating habits, and this influence lasts through adulthood. People make food choices based on how they see others and want others to see them. For example, individuals who are surrounded by others who consume fast food are more likely to do the same.
Health concerns. Some people have significant food allergies, to peanuts for example, and need to avoid those foods. Others may have developed health issues which require them to follow a low salt diet. In addition, people who have never worried about their weight have a very different approach to eating than those who have long struggled with excess weight.
Emotions. There is a wide range in how emotional issues affect eating habits. When faced with a great deal of stress, some people tend to overeat, while others find it hard to eat at all.
Green food/Sustainability choices. Based on a growing understanding of diet as a public and personal issue, more and more people are starting to make food choices based on their environmental impact. Realizing that their food choices help shape the world, many individuals are opting for a vegetarian diet, or, if they do eat animal products, striving to find the most “cruelty-free” options possible. Purchasing local and organic food products and items grown through sustainable products also help shrink the size of one’s dietary footprint.
558
Pause to Reflect
Think of your last meal or snack. What are some of the factors listed above that led you to choose to eat what you did?
Note
Vegetarian Diet
People choose a vegetarian diet for various reasons, including religious doctrines, health concerns, ecological and animal welfare concerns, or simply because they dislike the taste of meat. There are different types of vegetarians, but a common theme is that vegetarians do not eat meat. Four common forms of vegetarianism are:
Lacto-ovo vegetarian. This is the most common form. This type of vegetarian diet includes the animal foods eggs and dairy products.
Lacto-vegetarian. This type of vegetarian diet includes dairy products but not eggs.
Ovo-vegetarian. This type of vegetarian diet includes eggs but not dairy products.
Vegan. This type of vegetarian diet does not include dairy, eggs, or any type of animal product or animal by-product.
559
Preparing vegetarian meals will be addressed further in Chapter 15.
Achieving a Healthy Diet
Achieving a healthy diet is a matter of balancing the quality and quantity of food that is eaten. There are five key factors that make up a healthful diet:
A diet must be adequate, by providing sufficient amounts of each essential nutrient, as well as fiber and adequate calories.
A balanced diet results when you do not consume one nutrient at the expense of another, but rather get appropriate amounts of all nutrients.
Calorie control is necessary so that the amount of energy you get from the nutrients you consume equals the amount of energy you expend during your day’s activities.
Moderation means not eating to the extremes, neither too much nor too little.
Variety refers to consuming different foods from within each of the food groups on a regular basis.
A healthy diet is one that favors whole foods. As an alternative to modern processed foods, a healthy diet focuses on “real” fresh whole foods that have been sustaining people for generations. Whole foods supply the needed vitamins, minerals, protein, carbohydrates, fats, and fiber that are essential to good health. Commercially prepared and fast foods are often lacking nutrients and often contain inordinate amounts of sugar, salt, saturated and trans fats, all of which are associated with the development of diseases such as atherosclerosis, heart disease, stroke, cancer, obesity, diabetes, and other illnesses. A balanced diet is a mix of food from the different food groups (vegetables, legumes, fruits, grains, protein foods, and dairy).
Adequacy
An adequate diet is one that favors nutrient-dense foods. Nutrient-dense foods are defined as foods that contain many essential nutrients per calorie. Nutrient-dense foods are the opposite of “empty-calorie” foods, such as sugary carbonated beverages, which are also called “nutrient-poor.” Nutrient-dense foods include fruits and vegetables, lean meats, poultry, fish, low-fat dairy products, and whole grains. Choosing more nutrient-dense foods will facilitate weight loss, while simultaneously providing all necessary nutrients.
Balance
Balance the foods in your diet. Achieving balance in your diet entails not consuming one nutrient at the expense of another. For example, calcium is essential for healthy teeth and bones, but too much calcium will interfere with iron absorption. Most foods that are good sources of iron are poor sources of calcium, so in order to get the necessary amounts of calcium and iron from your diet, a proper balance between food choices is critical. Another example is that while sodium is an essential nutrient, excessive intake may contribute to congestive heart failure and chronic kidney disease in some people. Remember, everything must be consumed in the proper amounts.
Moderation
Eat in moderation. Moderation is crucial for optimal health and survival. Eating nutrient-poor foods each night for dinner will lead to health complications. But as part of an otherwise healthful diet and consumed only on a weekly basis, this should not significantly impact overall health. It’s important to remember that eating is, in part, about enjoyment and indulging with a spirit of moderation. This fits within a healthy diet.
Monitor food portions. For optimum weight maintenance, it is important to ensure that energy consumed from foods meets the energy expenditures required for body functions and activity. If not, the excess energy contributes to gradual, steady accumulation of stored body fat and weight gain. In order to lose body fat, you need to ensure that more calories are burned than consumed. Likewise, in order to gain weight, calories must be eaten in excess of what is expended daily.
Variety
Variety involves eating different foods from all the food groups. Eating a varied diet helps to ensure that you consume and absorb adequate amounts of all essential nutrients required for health. One of the major drawbacks of a monotonous diet is the risk of consuming too much of some nutrients and not enough of others. Trying new foods can also be a source of pleasure—you never know what foods you might like until you try them.
Developing a healthful diet can be rewarding, but be mindful that all of the principles presented must be followed to derive maximal health benefits. For instance, introducing variety in your diet can still result in the consumption of too many high-calorie, nutrient poor foods and inadequate nutrient intake if you do not also employ moderation and calorie control. Using all of these principles together will promote lasting health benefits.
561
Pause to Reflect
Think back to your childhood, how do you think your diet did with regards to adequacy, balance, moderation, and variety? What about your diet now?
There are many different programs that can support early care and education programs in providing nutritious meals and snacks for children. Let’s explore a few of these.
Child and Adult Care Food Program
The Child and Adult Care Food Program (CACFP) is a federal program that provides reimbursements for nutritious meals and snacks to eligible children and adults who are enrolled for care at participating child care centers, day care homes, and adult day care centers. Eligible public or private nonprofit child care centers, outside-school-hours care centers, Head Start programs, and other institutions which are licensed or approved to provide day care services may participate in CACFP, independently or as sponsored centers.
562
Over 2 billion meals are served in the CACFP.
563
Even if a program chooses not to participate in (or is ineligible for) the CACFP, they are required by licensing to its meal plan requirements.
564
(See Tables 12.4 and 12.5) The CACFP nutrition standards for meals and snacks served in the CACFP are based on the Dietary Guidelines for Americans, science-based recommendations made by the National Academy of Medicine, cost and practical considerations, and stakeholder’s input. Under these standards, meals and snacks served include a greater variety of vegetables and fruit, more whole grains, and less added sugar and saturated fat.
565
(See Table 12.6)
Table 12.4 – Infant Meal Patterns
566
Meal or snack
0-5 Months
6-11 Months
Breakfast
4-6 fl oz breastmilk or formula
6-8 fl oz breastmilk or formula
0-4 tbsp infant cereal, meat, fish, poultry, whole eggs, cooked dry beans or peas; or 0-2 oz cheese; or 0-4 oz (volume) cottage cheese; or 0-4 oz yogurt; or a combination*
0-2 tbsp vegetable, fruit or both*
Lunch or Supper
4-6 fl oz breastmilk or formula
6-8 fl oz breastmilk or formula
0-4 tbsp infant cereal, meat, fish, poultry, whole eggs, cooked dry beans or peas; or 0-2 oz cheese; or 0-4 oz (volume) cottage cheese; or 0-4 oz yogurt; or a combination*
0-2 tbsp vegetable, fruit or both*
Snack
4-6 fl oz breastmilk or formula
2-4 fl oz breastmilk or formula
0-½ bread slice; or 0-2 crackers; or 0-4 tbsp infant cereal or readyto-eat cereal*
0-2 tbsp vegetable, fruit or both*
Solid foods are required when infant is ready. All serving sizes are minimum quantities of the food components that are required to be served
Table 12.5 – Meal Pattern for
Children
567
Breakfast
Meal or snack
Food Item
1-2 Years
3-5 Years
6-18 Years
Breakfast
Milk
½ cup whole
¾ cup low-fat or fat-free
1 cup low-fat or fat-free
Vegetables, fruit, or both
¼ cup
½ cup
½ cup
Grains
½ ounce equivalent
½ ounce equivalent
1 ounce equivalent
Lunch or Supper
Meal or snack
Food Item
1-2 Years
3-5 Years
6-18 Years
Lunch or Supper
Milk
½ cup whole
¾ cup low-fat or fat-free
1 cup low-fat or fat-free
Meat and meat alternative
1 ounce
1½ ounces
2 ounces
Vegetables
1/8 cup
¼ cup
½ cup
Fruits
1/8 cup
¼ cup
¼ cup
Grains
½ ounce equivalent
½ ounce equivalent
1 ounce equivalent
Snack (choose 2 of the options)
Meal or snack
Food Item
1-2 Years
3-5 Years
6-18 Years
Snack
(choose 2 of the options)
Milk
½ cup whole
½ cup low-fat or fat-free
1 cup low-fat or fat-free
Meat and meat alternative
½ ounce
½ ounce
1 ounce
Vegetables
½ cup
½ cup
¾ cup
Fruits
½ cup
½ cup
¾ cup
Grains
½ ounce equivalent
½ ounce equivalent
1 ounce equivalent
Table 12.6 – CACFP Best Practices
568
,
569
Category
Best Practices
Vegetables and Fruit
Make at least one of the two required components of snack a vegetable or fruit
Serve a variety of fruit and choose whole fruits
Juice is limited to once a day
Provide at least one serving each of dark green leafy vegetables, red and orange vegetables, beans and peas (legumes), starchy vegetables, and other vegetables each week
Grains
Provide at least two servings of whole grains per day (at least one is required)
Meat and Meat Alternatives
Serve only lean meats, nuts, and legumes.
Limit serving processed meats to no more than one serving per week.
Serve only natural cheeses and choose low-fat or reduced fat-cheeses.
Milk
Serve only unflavored milk
Nondairy milk substitutes that are nutritionally equivalent to milk may be served in place of milk to children with medical or special dietary needs
Sugar
Yogurt must contain no more than 23 grams per 6 ounces
Breakfast cereals must contain no more than 6 grams of sugar per dry ounce
Avoid serving non-creditable foods that are sources of added sugars, such as sweet toppings (honey, jam, syrup), mix-in ingredients sold with yogurt, and sugar sweetened beverages
Miscellaneous
Frying is not allowed as a way of preparing foods on-site
Limit serving purchased pre-fired foods to no more than one serving per week
Incorporate seasonal and local produced foods into meals
“And all licensed child care providers…must follow the Healthy Beverages in Child Care Act. The four key messages in the Healthy Beverages in Child Care Act are:
Only unflavored, unsweetened, non-fat (fat free, skim, 0%) or low fat (1%) milk can be served to children 2 years of age or older.
No beverages with added sweeteners, natural or artificial, can be served, including sports drinks, sweet teas, juice drinks with added sugars, flavored milk, soda, and diet drinks.
A maximum of one serving of 100% juice is allowed per day.
Clean and safe drinking water must be readily available at all times; indoors and outdoors and with meals and snacks.”
570
Dietary Guidelines for Americans
The Dietary Guidelines for Americans provides evidence-based nutrition information and advice for people ages two and older to help Americans make healthy choices about food and beverages in their daily lives. The Guidelines also serve as the basis for federal food and nutrition education programs, like the MyPlate campaign.
The Dietary Guidelines for Americans, produced by HHS and the U.S. Department of Agriculture every five years, analyze the latest research to help Americans make smart choices about food and physical activity so they can live healthier lives.
The
2015-2020 Dietary Guidelines for Americans
focuses on making small shifts in your daily eating habits to improve your health over the long run. They also emphasize the importance of “eating patterns,” which refer to the combination of ALL foods and beverages a person consumes regularly over time, rather than focusing on individual nutrients or foods in isolation. Healthy eating patterns, along with regular physical activity, have been shown in a large body of current science to help people reach and maintain good health while reducing risks of chronic disease throughout their lives. Additionally, healthy eating patterns can be adapted to an individual’s budget, taste preferences, traditions, and culture.
The core recommendations for these healthy eating patterns are unchanged from previous editions of the Guidelines, and continue to encourage Americans to consume more healthy foods like vegetables, fruits, whole grains, fat-free and low-fat dairy products, lean meats, seafood, other protein foods, and oils. They also recommend limiting sodium, saturated and trans fats, and added sugars.
There are five overarching guidelines in this eighth edition:
Follow a healthy eating pattern across the lifespan. Eating patterns are the combination of foods and drinks that a person eats over time.
A variety of vegetables: dark green, red and orange, legumes (beans and peas), starchy and other vegetables.
Fruits, especially whole fruit.
Grains, at least half of which are whole grain.
Fat-free or low-fat dairy, including milk, yogurt, cheese, and/or fortified soy beverages.
A variety of protein foods, including seafood, lean meats and poultry, eggs, legumes (beans and peas), soy products, and nuts and seeds.
Oils, including those from plants: canola, corn, olive, peanut, safflower, soybean, and sunflower. Oils also are naturally present in nuts, seeds, seafood, olives, and avocados.
Focus on variety, nutrient-dense foods, and amount.
Limit calories from added sugars and saturated fats, and reduce sodium intake.
Children younger than 14 should consume less than 2.300 mg of sodium per day.
Less than 10% of daily calories should come from saturated fats.
Less than 10% of daily calories should come from added sugars
Shift to healthier food and beverage choices.
Support healthy eating patterns for all.
571
Physical Guidelines for Americans
The second edition of the
Physical Activity Guidelines for Americans
issued by the Department of Health and Human Services provides science-based guidance to help people ages 3 years and older improve their health through participation in regular physical activity. Key guidelines include:
Preschool-Aged Children
Preschool-aged children (ages 3 through 5 years) should be physically active throughout the day to enhance growth and development. Adult caregivers of preschool-aged children should encourage active play that includes a variety of activity types.
Children and Adolescents
It is important to provide young people opportunities and encouragement to participate in physical activities that are appropriate for their age, that are enjoyable, and that offer variety. Children and adolescents ages 6 through 17 years should do 60 minutes (1 hour) or more of moderate-to-vigorous physical activity daily that includes activity that is aerobic, muscle-strengthening, and bone-strengthening.
572
Physical activity will be addressed further in Chapter 13.
MyPlate
MyPlate is the United States Department of Agriculture’s food guidance program to help Americans eat healthy and is based on the Dietary Guidelines for America. It replaces MyPyramid (which had replaced the classic Food Guide Pyramid).
The visual for MyPlate is a familiar mealtime symbol, the plate. It gives easy visual reference to remind people to create balanced meals. The main messages of MyPlate include:
Make half the plate fruits and vegetables
Focus on whole fruits.
Vary your veggies.
Make half the grains whole grains.
Move to low-fat or fat-free milk or yogurt.
Vary the sources of protein.
573
1992: Food Guide Pyramid
2005: MyPyramid Food Guidance System
2011: MyPlate
12.5 – The most recent Food Guides from the USDA.
574
Dietary Reference Intakes (DRI)
Issued by the Food and Nutrition Board of the Institute of Medicine, National Academy of Sciences, the DRI is the general term for a set of reference values used to plan and assess nutrient intakes of healthy people. These values, which vary by age and sex, include:
Recommended Dietary Allowance (RDA): average daily level of intake sufficient to meet the nutrient requirements of nearly all (97%-98%) healthy people.
Adequate Intake (AI): established when evidence is insufficient to develop an RDA and is set at a level assumed to ensure nutritional adequacy.
Tolerable Upper Intake Level (UL): maximum daily intake unlikely to cause adverse health effects.
575
That information is used to create nutrition fact labels.
Nutrition Facts Labels
The information in the main or top section (see #1-4) of the sample nutrition label (below) can vary with each food and beverage product; it contains product-specific information (serving size, calories, and nutrient information). The bottom section contains a footnote that explains the % Daily Value and gives the number of calories used for general nutrition advice.
In the following Nutrition Facts label certain sections have been colored to help focus on those areas that will be explained in detail. Note that these colored sections are not on the actual food labels of products you purchase.
1. Serving Information
When looking at the Nutrition Facts label, first take a look at the number of servings in the package (servings per container) and the serving size. Serving sizes are standardized to make it easier to compare similar foods; they are provided in familiar units, such as cups or pieces, followed by the metric amount, e.g., the number of grams (g). The serving size reflects the amount that people typically eat or drink
.
It is not a recommendation of how much you should eat or drink.
12.7 – The serving information portion of the example nutrition label for lasagna.
577
It’s important to realize that all the nutrient amounts shown on the label, including the number of calories, refer to the size of the serving. Pay attention to the serving size, especially how many servings there are in the food package. For
example, you might ask yourself if you are consuming ½ serving, 1 serving, or more.
2. Calories
Calories provide a measure of how much energy you get from a serving of this food.
12.8 – The calories per serving portion of the example nutrition label for lasagna.
578
In the example, there are
280 calories
in one serving of lasagna. What if you ate the entire package? Then, you would consume 4 servings, or
1,120 calories
.
3. Nutrients
12.9 – The portion of the example nutrition label for lasagna that details nutrients.
579
Look at section 3 in the sample label (shown in Table 12.9). It shows you some key nutrients that impact your health. Two key facts about the nutrients:
Nutrients to get less of: Saturated Fat, Sodium, and Added Sugars.
Nutrients to get more of: Dietary Fiber, Vitamin D, Calcium, Iron, and Potassium.
4. The Percent Daily Value (%DV)
The % Daily Value (%DV) is the percentage of the Daily Value for each nutrient in a serving of the food. The Daily Values are reference amounts (expressed in grams, milligrams, or micrograms) of nutrients to consume or not to exceed each day
.
12.10 – The portion of the example nutrition label that details the percent daily value of the nutrients.
580
The %DV shows how much a nutrient in a serving of a food contributes to a total daily diet for
adults
. The %DV helps you determine if a serving of food is high or low in a nutrient.
581
Pause to Reflect
Find a food that is marketed to young children (that has a food label). Looking at the label, how do you think it rates a healthy choice? Why?
The federal government provides federal assistance to schools to provide nutritious meals to children. With the exception of the Special Milk Program, early care and education programs will not qualify for these programs. But they are included in this chapter as they are important sources of nutrition for many children in the U.S., for reference for those that may work within the school system, and they may provide resources that early care and education programs may find useful when planning healthy meals and snacks and purchasing foods.
National School Lunch Program
The National School Lunch Program (NSLP) is a federally assisted meal program operating in public and nonprofit private schools and residential child care institutions. It provides nutritionally balanced, low-cost or no-cost lunches to children each school day. The program was established under the Richard B. Russell National School Lunch Act, signed into law by President Harry Truman in 1946. 30.4 million children participated in the program in 2016.
582
School Breakfast Program
The School Breakfast Program (SBP) is a federally assisted meal program operating in public and non-profit private schools and residential child care institutions. The SBP started in 1966 as a pilot project, and was made a permanent entitlement program by Congress in 1975. Participation in the SBP has slowly but steadily grown over the years and in 2016, 14.57 million children participated in the program.
584
Special Milk Program
The Special Milk Program provides milk to children in schools, child care program and eligible camps that do not participate in other federal child nutrition meal service programs. The program reimburses schools and institutions for the milk they serve. In 2011, 3,848 schools and residential child care institutions participated, along with 782 summer camps and 527 non‐residential child care institutions. Schools in the National School Lunch or School Breakfast Programs may also participate in the Special Milk Program to provide milk to children in half‐day pre‐kindergarten and kindergarten programs where children do not have access to the school meal programs.
585
Summer Food Service Program
The Summer Food Service Program (SFSP) provides free meals and snacks when school is not in session. The seasonal nature of SFSP, and the diversity of sponsors and site operators, make it unique. State agencies, sponsors, and community organizations need flexibility to operate the SFSP in a manner that is responsive to local conditions and allows operators to focus on ensuring children in need can access food when school is not in session. In the summer of 2018 over 145 million meals were served to over 2.6 million children.
586
Assessing Quality of Meal and Snack Times
Just like with safety and health (and many other things), early care and education programs should assess how well they are meeting children’s nutritional needs with the meals and snacks they are providing for children. An assessment, such as one in Appendix N can be used to help programs do this. You will notice that providing a positive eating environment takes more than just giving children healthy food. Chapter 14 will look more at this by age.
Summary
Providing nutritious meals and snacks to children in early care and education programs requires a basic understanding of nutrition. Program staff should also have an understanding of what a complete and healthy diet includes and how to address factors that influence food choices, to ensure that they provide healthy food and beverages that children will enjoy eating. Being aware of the programs available to support doing so is also valuable. Children that have high-quality meal and snack times will have the fuel their bodies need to sustain optimal growth and development.


5.5: The Uniform Distribution
-
- Last updated
- Save as PDF
- Zoya Kravets
- Mission College
The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.
Example 5.3.1
The data in Table \(\PageIndex{1}\) are 55 smiling times, in seconds, of an eight-week-old baby.
| 10.4 | 19.6 | 18.8 | 13.9 | 17.8 | 16.8 | 21.6 | 17.9 | 12.5 | 11.1 | 4.9 |
| 12.8 | 14.8 | 22.8 | 20.0 | 15.9 | 16.3 | 13.4 | 17.1 | 14.5 | 19.0 | 22.8 |
| 1.3 | 0.7 | 8.9 | 11.9 | 10.9 | 7.3 | 5.9 | 3.7 | 17.9 | 19.2 | 9.8 |
| 5.8 | 6.9 | 2.6 | 5.8 | 21.7 | 11.8 | 3.4 | 2.1 | 4.5 | 6.3 | 10.7 |
| 8.9 | 9.4 | 9.4 | 7.6 | 10.0 | 3.3 | 6.7 | 7.8 | 11.6 | 13.8 | 18.6 |
The sample mean = 11.49 and the sample standard deviation = 6.23.
We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution.
Let \(X =\) length, in seconds, of an eight-week-old baby's smile.
The notation for the uniform distribution is
\(X \sim U(a, b)\) where \(a =\) the lowest value of \(x\) and \(b =\) the highest value of \(x\).
The probability density function is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\).
For this example, \(X \sim U(0, 23)\) and \(f(x) = \frac{1}{23-0}\) for \(0 \leq X \leq 23\).
Formulas for the theoretical mean and standard deviation are
\[\mu = \frac{a+b}{2} \nonumber\]
and
\[\sigma = \sqrt{\frac{(b-a)^{2}}{12}} \nonumber\]
For this problem, the theoretical mean and standard deviation are
\[\mu = \frac{0+23}{2} = 11.50 \, seconds \nonumber\]
and
\[\sigma = \frac{(23-0)^{2}}{12} = 6.64\, seconds. \nonumber\]
Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.
Exercise \(\PageIndex{1}\)
The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of a and \(b\). Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.
| 1 | 12 | 4 | 10 | 4 | 14 | 11 |
| 7 | 11 | 4 | 13 | 2 | 4 | 6 |
| 3 | 10 | 0 | 12 | 6 | 9 | 10 |
| 5 | 13 | 4 | 10 | 14 | 12 | 11 |
| 6 | 10 | 11 | 0 | 11 | 13 | 2 |
Answer
\(a\) is zero; \(b\) is \(14\); \(X \sim U (0, 14)\); \(\mu = 7\) passengers; \(\sigma = 4.04\) passengers
Example 5.3.2A
a. Refer to Example 5.3.1. What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds?
Answer
a. Find \(P(2 < x < 18)\).
\(P(2 < x < 18) = (\text{base})(\text{height}) = (18 – 2)\left(\frac{1}{23}\right) = \left(\frac{16}{23}\right)\).
Figure \(\PageIndex{1}\) This graph shows a uniform distribution. The horizontal axis ranges from 0 to 15. The distribution is modeled by a rectangle extending from x = 0 to x = 15. A region from x = 2 to x = 18 is shaded inside the rectangle.Exercise \(\PageIndex{2}\)B
b. Find the 90 th percentile for an eight-week-old baby's smiling time.
Answer
b. Ninety percent of the smiling times fall below the 90 th percentile, \(k\), so \(P(x < k) = 0.90\)
\[P(x < k)= 0.90\]
\[(\text{base})(\text{height}) = 0.90\]
\[(k−0)\left(\frac{1}{23}\right) = 0.90\]
\[k = (23)(0.90) = 20.7\]
Figure \(\PageIndex{2}\) This shows the graph of the function f(x) = 1/15. A horiztonal line ranges from the point (0, 1/15) to the point (15, 1/15). A vertical line extends from the x-axis to the end of the line at point (15, 1/15) creating a rectangle. A region is shaded inside the rectangle from x = 0 to x = k. The shaded area represents P(x < k) = 0.90.Exercise \(\PageIndex{3}\)C
c. Find the probability that a random eight-week-old baby smiles more than 12 seconds KNOWING that the baby smiles MORE THAN EIGHT SECONDS .
Answer
c. This probability question is a conditional . You are asked to find the probability that an eight-week-old baby smiles more than 12 seconds when you already know the baby has smiled for more than eight seconds.
Find \(P(x > 12 | x > 8)\) There are two ways to do the problem. For the first way , use the fact that this is a conditional and changes the sample space. The graph illustrates the new sample space. You already know the baby smiled more than eight seconds.
Write a new \(f(x): f(x) = \frac{1}{23-8} = \frac{1}{15}\)
for \(8 < x < 23\)
\(P(x > 12 | x > 8) = (23 − 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)\)
Figure \(\PageIndex{3}\) f(X)=1/15 graph displaying a boxed region consisting of a horizontal line extending to the right from point 1/15 on the y-axis, a vertical upward line from points 8 and 23 on the x-axis, and the x-axis. A shaded region from points 12-23 occurs within this area.For the second way , use the conditional formula from Probability Topics with the original distribution \(X \sim U(0, 23)\):
\(P(\text{A|B}) = \frac{P(\text{A AND B})}{P(\text{B})}\)
For this problem, \(\text{A}\) is (\(x > 12\)) and \(\text{B}\) is (\(x > 8\)).
So, \(P(x > 12|x > 8) = \frac{(x > 12 \text{ AND } x > 8)}{P(x > 8)} = \frac{P(x > 12)}{P(x > 8)} = \frac{\frac{11}{23}}{\frac{15}{23}} = \frac{11}{15}\)
Figure \(\PageIndex{4}\): Darker shaded area represents \(P(x > 12)\). Entire shaded area shows \(P(x > 8)\).Exercise \(\PageIndex{2}\)
A distribution is given as \(X \sim U(0, 20)\). What is \(P(2 < x < 18)\)? Find the 90 th percentile.
Answer
\(P(2 < x < 18) = 0.8\); 90 th percentile \(= 18\)
Example 5.3.3
The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive.
Exercise \(\PageIndex{3}\).1
a. What is the probability that a person waits fewer than 12.5 minutes?
Answer
a. Let \(X =\) the number of minutes a person must wait for a bus. \(a = 0\) and \(b = 15\). \(X \sim U(0, 15)\). Write the probability density function. \(f(x) = \frac{1}{15-0} = \frac{1}{15}\) for \(0 \leq x \leq 15\).
Find \(P(x < 12.5)\). Draw a graph.
\[P(x < k) = (\text{base})(\text{height}) = (12.5−0)\left(\frac{1}{15}\right) = 0.8333\]
The probability a person waits less than 12.5 minutes is 0.8333.
Figure \(\PageIndex{5}\). This shows the graph of the function f(x) = 1/15. A horiztonal line ranges from the point (0, 1/15) to the point (15, 1/15). A vertical line extends from the x-axis to the end of the line at point (15, 1/15) creating a rectangle. A region is shaded inside the rectangle from x = 0 to x = 12.5.Exercise \(\PageIndex{3}\).2
b. On the average, how long must a person wait? Find the mean, \(\mu\), and the standard deviation, \(\sigma\).
Answer
b. \(\mu = \frac{a+b}{2} = \frac{15+0}{2} = 7.5\). On the average, a person must wait 7.5 minutes.
\(\sigma = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(12-0)^{2}}{12}} = 4.3\). The Standard deviation is 4.3 minutes.
Exercise \(\PageIndex{3}\).3
c. Ninety percent of the time, the time a person must wait falls below what value?
Note <IP_ADDRESS>.1
This asks for the 90 th percentile.
Answer
c. Find the 90 th percentile. Draw a graph. Let \(k =\) the 90 th percentile.
\(P(x < k) = (\text{base})(\text{height}) = (k−0)\left(\frac{1}{15}\right)\)
\(0.90 = (k)\left(\frac{1}{15}\right)\)
\(k = (0.90)(15) = 13.5\)
\(k\) is sometimes called a critical value.
The 90
th
percentile is 13.5 minutes. Ninety percent of the time, a person must wait at most 13.5 minutes.
Exercise \(\PageIndex{4}\)
The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive.
- Find \(a\) and \(b\) and describe what they represent.
- Write the distribution.
- Find the mean and the standard deviation.
- What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours?
- What is the 65 th percentile for the duration of games for a team for the 2011 season?
Answer
- \(a\) is \(447\), and \(b\) is \(521\). a is the minimum duration of games for a team for the 2011 season, and \(b\) is the maximum duration of games for a team for the 2011 season.
- \(X \sim U(447, 521)\).
- \(\mu = 484\), and \(\sigma = 21.36\)
- \(P(480 < x < 500) = 0.2703\)
- 65 th percentile is 495.1 hours.
Example 5.3.4
Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. Let \(X =\) the time, in minutes, it takes a nine-year old child to eat a donut. Then \(X \sim U(0.5, 4)\).
a. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______.
Solution
a. 0.5714
Exercise \(\PageIndex{4}\).1
b. Find the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes.
The second question has a conditional probability. You are asked to find the probability that a nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. Solve the problem two different ways (see Example ). You must reduce the sample space. First way : Since you know the child has already been eating the donut for more than 1.5 minutes, you are no longer starting at a = 0.5 minutes. Your starting point is 1.5 minutes.
Write a new \(f(x)\):
\(f(x) = \frac{1}{4-1.5} = \frac{2}{5}\) for \(1.5 \leq x \leq 4\).
Find \(P(x > 2|x > 1.5)\). Draw a graph.
Figure \(\PageIndex{2}\).f(X)=2/5 graph displaying a boxed region consisting of a horizontal line extending to the right from point 2/5 on the y-axis, a vertical upward line from points 1.5 and 4 on the x-axis, and the x-axis. A shaded region from points 2-4 occurs within this area.\(P(x > 2|x > 1.5) = (\text{base})(\text{new height}) = (4 − 2)(25)\left(\frac{2}{5}\right) =\) ?
Answer
b. \(\frac{4}{5}\)
The probability that a nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes is \(\frac{4}{5}\).
Second way: Draw the original graph for \(X \sim U(0.5, 4)\). Use the conditional formula
\(P(x > 2 | x > 1.5) = \frac{P(x > 2 \text{AND} x > 1.5)}{P(x > 1.5)} = \frac{P(x>2)}{P(x>1.5)} = \frac{\frac{2}{3.5}}{\frac{2.5}{3.5}} = 0.8 = \frac{4}{5}\)
Exercise \(\PageIndex{5}\)
Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Let \(X =\) the time, in minutes, it takes a student to finish a quiz. Then \(X \sim U(6, 15)\).
Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes.
Answer
\(P(x > 8) = 0.7778\)
\(P(x > 8 | x > 7) = 0.875\)
Example 5.3.5
Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and four hours. Let \(x =\) the time needed to fix a furnace. Then \(x \sim U(1.5, 4)\).
- Find the probability that a randomly selected furnace repair requires more than two hours.
- Find the probability that a randomly selected furnace repair requires less than three hours.
- Find the 30 th percentile of furnace repair times.
- The longest 25% of furnace repair times take at least how long? (In other words: find the minimum time for the longest 25% of repair times.) What percentile does this represent?
- Find the mean and standard deviation
Solution
a. To find \(f(x): f(x) = \frac{1}{4-1.5} = \frac{1}{2.5}\) so \(f(x) = 0.4\)
\(P(x > 2) = (\text{base})(\text{height}) = (4 – 2)(0.4) = 0.8\)
Figure \(\PageIndex{3}\). Uniform Distribution between 1.5 and four with shaded area between two and four representing the probability that the repair time \(x\) is greater than twob. \(P(x < 3) = (\text{base})(\text{height}) = (3 – 1.5)(0.4) = 0.6\)
The graph of the rectangle showing the entire distribution would remain the same. However the graph should be shaded between \(x = 1.5\) and \(x = 3\). Note that the shaded area starts at \(x = 1.5\) rather than at \(x = 0\); since \(X \sim U(1.5, 4)\), \(x\) can not be less than 1.5.
Figure \(\PageIndex{4}\). Uniform Distribution between 1.5 and four with shaded area between 1.5 and three representing the probability that the repair time \(x\) is less than threec.
Figure \(\PageIndex{5}\). Uniform Distribution between 1.5 and 4 with an area of 0.30 shaded to the left, representing the shortest 30% of repair times.
\(P(x < k) = 0.30\)
\(P(x < k) = (\text{base})(\text{height}) = (k – 1.5)(0.4)\)
\(0.3 = (k – 1.5) (0.4)\)
; Solve to find \(k\):
\(0.75 = k – 1.5\), obtained by dividing both sides by 0.4
\(k = 2.25\)
, obtained by adding 1.5 to both sides
The 30 th percentile of repair times is 2.25 hours. 30% of repair times are 2.25 hours or less.
d.
Figure \(\PageIndex{6}\). Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times.
\(P(x > k) = 0.25\)
\(P(x > k) = (\text{base})(\text{height}) = (4 – k)(0.4)\)
\(0.25 = (4 – k)(0.4)\)
; Solve for \(k\):
\(0.625 = 4 − k\),
obtained by dividing both sides by 0.4
\(−3.375 = −k\),
obtained by subtracting four from both sides:
\(k = 3.375\)
The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer).
Note: Since 25% of repair times are 3.375 hours or longer, that means that 75% of repair times are 3.375 hours or less. 3.375 hours is the 75 th percentile of furnace repair times.
e. \(\mu = \frac{a+b}{2}\) and \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\)
\(\mu = \frac{1.5+4}{2} = 2.75\) hours and \(\sigma = \sqrt{\frac{(4-1.5)^{2}}{12}} = 0.7217\) hours
Exercise \(\PageIndex{6}\)
The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. Let \(X =\) the time needed to change the oil on a car.
- Write the random variable \(X\) in words. \(X =\) __________________.
- Write the distribution.
- Graph the distribution.
- Find \(P(x > 19)\).
- Find the 50 th percentile.
Answer
- Let \(X =\) the time needed to change the oil in a car.
- \(X \sim U(11, 21)\).
- \(P(x > 19) = 0.2\)
- the 50 th percentile is 16 minutes.
Review
If \(X\) has a uniform distribution where \(a < x < b\) or \(a \leq x \leq b\), then \(X\) takes on values between \(a\) and \(b\) (may include \(a\) and \(b\)). All values \(x\) are equally likely. We write \(X \sim U(a, b)\). The mean of \(X\) is \(\mu = \frac{a+b}{2}\). The standard deviation of \(X\) is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\). The probability density function of \(X\) is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). The cumulative distribution function of \(X\) is \(P(X \leq x) = \frac{x-a}{b-a}\). \(X\) is continuous.
Figure \(\PageIndex{8}\).The probability \(P(c < X < d)\) may be found by computing the area under \(f(x)\), between \(c\) and \(d\). Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height.
Formula Review
\(X =\) a real number between \(a\) and \(b\) (in some instances, \(X\) can take on the values \(a\) and \(b\)). \(a =\) smallest \(X\); \(b =\) largest \(X\)
\(X \sim U(a, b)\)
The mean is \(\mu = \frac{a+b}{2}\)
The standard deviation is \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\)
Probability density function: \(f(x) = \frac{1}{b-a} \text{for} a \leq X \leq b\)
Area to the Left of \(x\): \(P(X < x) = (x – a)\left(\frac{1}{b-a}\right)\)
Area to the Right of \(x\): P(\(X\) > \(x\)) = (b – x)\(\left(\frac{1}{b-a}\right)\)
Area Between \(c\) and \(d\): \(P(c < x < d) = (\text{base})(\text{height}) = (d – c)\left(\frac{1}{b-a}\right)\)
Uniform: \(X \sim U(a, b)\) where \(a < x < b\)
- pdf: \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\)
- cdf: \(P(X \leq x) = \frac{x-a}{b-a}\)
- mean \(\mu = \frac{a+b}{2}\)
- standard deviation \(\sigma = \sqrt{\frac{(b-a)^{2}}{12}}\)
- \(P(c < X < d) = (d – c)\left(\frac{1}{b-a}\right)\)
References
McDougall, John A. The McDougall Program for Maximum Weight Loss. Plume, 1995.
Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
| 1.5 | 2.4 | 3.6 | 2.6 | 1.6 | 2.4 | 2.0 |
| 3.5 | 2.5 | 1.8 | 2.4 | 2.5 | 3.5 | 4.0 |
| 2.6 | 1.6 | 2.2 | 1.8 | 3.8 | 2.5 | 1.5 |
| 2.8 | 1.8 | 4.5 | 1.9 | 1.9 | 3.1 | 1.6 |
The sample mean = 2.50 and the sample standard deviation = 0.8302.
The distribution can be written as \(X \sim U(1.5, 4.5)\).
Exercise \(\PageIndex{7}\)
What type of distribution is this?
Exercise \(\PageIndex{8}\)
In this distribution, outcomes are equally likely. What does this mean?
Answer
It means that the value of x is just as likely to be any number between 1.5 and 4.5.
Exercise \(\PageIndex{9}\)
What is the height of \(f(x)\) for the continuous probability distribution?
Exercise \(\PageIndex{10}\)
What are the constraints for the values of \(x\)?
Answer
\(1.5 \leq x \leq 4.5\)
Exercise \(\PageIndex{11}\)
Graph \(P(2 < x < 3)\).
Exercise \(\PageIndex{12}\)
What is \(P(2 < x < 3)\)?
Answer
0.3333
Exercise \(\PageIndex{13}\)
What is \(P(x < 3.5 | x < 4)\)?
Exercise \(\PageIndex{14}\)
What is \(P(x = 1.5)\)?
Answer
zero
Exercise \(\PageIndex{15}\)
What is the 90 th percentile of square footage for homes?
Exercise \(\PageIndex{16}\)
Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet.
Answer
0.6
Exercise \(\PageIndex{17}\)
What is \(a\)? What does it represent?
Exercise \(\PageIndex{18}\)
What is \(b\)? What does it represent?
Answer
\(b\) is \(12\), and it represents the highest value of \(x\).
Exercise \(\PageIndex{19}\)
What is the probability density function?
Exercise \(\PageIndex{20}\)
What is the theoretical mean?
Answer
six
Exercise \(\PageIndex{21}\)
What is the theoretical standard deviation?
Exercise \(\PageIndex{22}\)
Draw the graph of the distribution for \(P(x > 9)\).
Answer
Figure \(\PageIndex{9}\).Exercise \(\PageIndex{23}\)
Find \(P(x > 9)\).
Exercise \(\PageIndex{24}\)
Find the 40 th percentile.
Answer
4.8
Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.
Exercise \(\PageIndex{25}\)
What is being measured here?
Exercise \(\PageIndex{26}\)
In words, define the random variable \(X\).
Answer
\(X\) = The age (in years) of cars in the staff parking lot
Exercise \(\PageIndex{27}\)
Are the data discrete or continuous?
Exercise \(\PageIndex{28}\)
The interval of values for \(x\) is ______.
Answer
0.5 to 9.5
Exercise \(\PageIndex{29}\)
The distribution for \(X\) is ______.
Exercise \(\PageIndex{30}\)
Write the probability density function.
Answer
\(f(x) = \frac{1}{9}\) where \(x\) is between 0.5 and 9.5, inclusive.
Exercise \(\PageIndex{31}\)
Graph the probability distribution.
-
Sketch the graph of the probability distribution.
Figure \(\PageIndex{10}\).
-
Identify the following values:
- Lowest value for \(\bar{x}\): _______
- Highest value for \(\bar{x}\): _______
- Height of the rectangle: _______
- Label for x -axis (words): _______
- Label for y -axis (words): _______
Exercise \(\PageIndex{32}\)
Find the average age of the cars in the lot.
Answer
\(\mu\) = 5
Exercise \(\PageIndex{33}\)
Find the probability that a randomly chosen car in the lot was less than four years old.
-
Sketch the graph, and shade the area of interest.
Figure \(\PageIndex{11}\).
- Find the probability. \(P(x < 4) =\) _______
Exercise \(\PageIndex{34}\)
Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old.
-
Sketch the graph, shade the area of interest.
Figure \(\PageIndex{12}\).
- Find the probability. \(P(x < 4 | x < 7.5) =\) _______
Answer
- Check student’s solution.
- \(\frac{3.5}{7}\)
Exercise \(\PageIndex{35}\)
What has changed in the previous two problems that made the solutions different
Exercise \(\PageIndex{36}\)
Find the third quartile of ages of cars in the lot. This means you will have to find the value such that \(\frac{3}{4}\), or 75%, of the cars are at most (less than or equal to) that age.
-
Sketch the graph, and shade the area of interest.
Figure \(\PageIndex{13}\).
- Find the value \(k\) such that \(P(x < k) = 0.75\).
- The third quartile is _______
Answer
- Check student's solution.
- \(k = 7.25\)
- \(7.25\)
Glossary
- Conditional Probability
- the likelihood that an event will occur given that another event has already occurred


2.2: Introduction to The History of Management
Be able to answer these questions:
- Describe management in the ancient world.
- How did the Italian Renaissance affect the progression of management theory?
- How did the Industrial Revolution affect the progression of management theory?
- How did Frederick Winslow Taylor influence management theory, and how did efficiency in management affect current management theory?
- How do bureaucratic and administrative management complement scientific management?
- How did Elton Mayo influence management theory, and how did the human relations movement affect current management theory?
- How did contingency and systems management transform management thought?
Michael Porter, Harvard Professor and Management Consultant, The Monitor Group. Michael Porter is the Bishop William Lawrence University Professor at Harvard Business School and one of the foremost scholars and consultants in business strategy. Dubbed the first “Lord of Strategy,” he is one of the most influential management thinkers of all time. Porter’s primary contribution is in the field of competition, specifically the question of why some companies profit while others do not. Porter first became interested in competition because of his enthusiasm for competing in youth sports (baseball, football, and basketball). Porter was born in 1947 and graduated from Princeton in 1969 with a degree in aerospace and mechanical engineering. He received his MBA from Harvard Business School in 1971 and his Ph.D. in business economics from Harvard University in 1973. His book Competitive Strategy: Techniques for Analyzing Industries and Competitors (published in 1980) was deemed the ninth most influential work of the 20th century by the Fellows of the Academy of Management. Porter, writing during a period of great economic competition between the United States and Japan, gained a vast audience for his work.
In his 1979 Harvard Business Review article “How Competitive Forces Shape Strategy,” Porter presented his game management idea that five forces help determine profitability. The five forces are competition in the industry, the potential of new entrants, the power of suppliers, the power of customers, and the threat of substitute products. An unattractive industry is one in which the five forces align to produce a purely competitive industry. In this type of industry, normal profit levels are the highest a firm can expect, which means that it can cover its costs and make the owner a profit but cannot make excess profits. Once a firm identifies the five forces in its industry, it can choose between three generic strategies for success: focus, differentiation, or cost leadership. Depending on where a firm is positioned within the market, the marketplace will determine its strategy. This “five forces, three strategies” framework explains how McDonald’s, Morton’s Steakhouse, Subway, Wendy’s, and TGIF can all be in the same industry and still be profitable. They offer different types of products to different types of customers. These products compete on price, differentiation, focus, or a combination. In addition to the five forces model, Porter developed the value-chain model, which describes the unique activities that a corporation performs to make its products valuable to its customers. Porter has also contributed to healthcare management, environmental regulation, international competition, and industry-level profits.
Porter’s five forces framework is intuitive and has provided managers with an approach to developing actual strategies. His ideas became popular because business leaders wanted to know how their companies could compete. Before Porter, management scholars stressed the idiosyncratic nature of business, stressing how each situation faced by each business was different. Other scholars offered business strategy models that were not as useful or practical as Porter’s. Through his use of industrial-organizational economics and his training in the case method, Porter bridged the gap between theoretical frameworks and the reality of the competitive business world and became one of the most important thinkers on business in the world.
Sources:
Bedeian, A.G. and Wren, D. A. (2001). Most influential management books of the 20th century. Organizational Dynamics, 29 (3): 221–225.
Kiechel, W. (2010). The lords of strategy: The secret intellectual history of the new corporate world. Harvard Business Review Press.
Magretta, J. (2011). Understanding Michael Porter: The essential guide to competition and strategy. Harvard Business Review Press.
Mathews, J. (2013). The competitive advantage of Michael Porter. In The Oxford handbook of management theorists. Oxford University Press.
While you may think that management is a relatively new field, it actually has its roots in the ancient world. In fact, whenever and wherever there has been commerce, there has been management and those thinking about how to do it better. For example, the Seven Wonders of the Ancient World, including the Colossus of Rhodes, the Hanging Gardens of Babylon, and the Great Pyramid, could only have been constructed through the work of a great many people. The size and complexity of these structures suggest that there must have been people (managers) who coordinated the labor and resources needed to execute the construction plans. Similarly, the Romans and the ancient Chinese could not have managed their vast empires without management, nor could the Phoenicians and the Greeks have dominated oceangoing trade without management.
Because management has been around for a while, it makes sense that the study of management is old. This idea is supported by the many managerial insights we can find in political, diplomatic, and military history and in philosophy, poetry, economics, and literature. Anyone familiar with Shakespeare’s King Lear would recognize the present-day management problem of succession planning! Modern managers have been influenced by the works of Chinese military strategist and philosopher Sun Tzu, Roman general and politician Julius Caesar, and even Genghis Kahn, Mongolian conqueror and ruler of what became the largest land empire in all of history (Jackson, 2014). Mark Zuckerberg of Facebook is a modern admirer of the Caesars and has said that he bases some of his management style on his classical education (Vargas, 2010).
Despite its ancient roots, modern management is less than 150 years old. In fact, a comparison of management before and after the Industrial Revolution shows that the former is only a shadowy comparison to the latter. Before the Industrial Revolution, work was performed, with exceptions, mostly in homes and on farms by forced labor (slaves or indentured servants) or family members, and the output they produced was often for employers’, local, or family consumption. Over the centuries, economics and morality shifted, and laborers could choose where and for whom to work. These changes, in turn, would bring about many changes in how labor and other resources were employed in production.
The two developments that transformed management were the revolutions in how and where goods were sold and the Industrial Revolution. The events combined led to selling a wider variety of goods to a wider variety of customers in more distant locations. These events also led to the establishment of vast companies. Competition required the development of economies of scale (i.e., increased production, lowering costs) and required coordination and specialization in the use of resources. The combination of coordination and specialization problems encouraged the development of management study as a distinct field.
In this chapter, we trace the evaluation of management from its origins in the ancient world to its form as a modern profession. Understanding how management came to be helps us understand its principles in a richer, more thorough context and understand how each concept we discuss is based on evidence produced by a wide range of scholars over many years in engineering, economics, psychology, sociology, and anthropology.
TOYOTA CASE STUDY VIDEO
Toyota is an excellent company case study that provides insight into the importance of management. You will see how Toyota's Production System (TPS) has significantly impacted manufacturing and is often called a "lean" or "Just-In-Time" system. TPS is based on two main concepts that aim to eliminate waste and achieve efficiency. Toyota’s “just in Time” management system changed how the world makes products.


1.19.3: Real Gases: Liquefaction of Gases
In the nineteenth century a major theme in science concerned the properties of gases and their liquefaction. The challenge offered by the liquefaction of gases also prompted the development of thermodynamics and the production of low temperatures. Michael Faraday is noteworthy in this context. In 1823 Faraday had liquefied chlorine, ammonia and sulfur dioxide using a combination of pressure and low temperatures [1].
Based on the observation that the densities of liquids are higher than gases the expectation was that liquefaction of a given gas would follow application of high pressure. However this turned out not to be the case. For example, Newton showed that application of 2790 atmospheres (\(\equiv 2.8 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}\)) did not liquefy air. In 1877 Cailletet and Pictet working independently obtained a mist of oxygen by sudden expansion of gas compressed at 300 atmospheres (\(\equiv 3 \times 10^{7} \mathrm{~N} \mathrm{~m}^{-2}\)) and cooled by \(\mathrm{CO}_{2}(\mathrm{s})\). However in developing the background to this subject we turn attention to the work of Joule.
Experiments by Joule
A gas, chemical substance \(j\), is held in a closed system. The molar thermodynamic energy \(\mathrm{U}_{j}\) is defined by equation (a) where \(\mathrm{V}_{j}\) is the molar volume and \(\mathrm{T}\), the temperature.
\[\mathrm{U}_{\mathrm{j}}=\mathrm{U}_{\mathrm{j}}\left[\mathrm{T}, \mathrm{V}_{\mathrm{j}}\right] \nonumber \]
The complete differential of equation (a) describes the change in \(\mathrm{U}_{\mathrm{j}}, \mathrm{dU}_{\mathrm{j}}\), as a function of temperature and volume.
\[\mathrm{dU}_{\mathrm{j}}=\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{T}}\right)_{\mathrm{v}} \, \mathrm{dT}+\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{V}_{\mathrm{j}}}\right)_{\mathrm{T}} \, \mathrm{dV}_{\mathrm{j}} \nonumber \]
The molar isochoric heat capacity \(\mathrm{C}_{\mathrm{Vj}}\) is defined by equation (c).
\[\mathrm{C}_{\mathrm{Vj}}=\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{T}}\right)_{\mathrm{V}} \nonumber \]
The first law of thermodynamics relates the change in \(\mathrm{U}_{j}\) to the work done on the system \(\mathrm{w}\) and heat \(\mathrm{q}\) passing from the surroundings into the system. Thus,
\[\mathrm{dU}_{\mathrm{j}}=\mathrm{q}+\mathrm{w} \nonumber \]
Hence,
\[\mathrm{q}=\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{T}}\right)_{\mathrm{V}} \, \mathrm{dT}+\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{V}_{\mathrm{j}}}\right)_{\mathrm{T}} \, \mathrm{dV} \mathrm{V}_{\mathrm{j}}-\mathrm{w} \nonumber \]
The apparatus used by Joule comprised two linked vessels having equal volumes. A tube joining the two vessels included a tap. In an experiment, one vessel was filled with gas \(j\) at a known pressure whereas the second vessel was evacuated. When the tap was opened gas flowed into the second vessel, equalizing the pressure in the two vessels. By flowing into an evacuated vessel the gas did no work because there was no confining pressure; i.e. \(\mathrm{w} =\) zero. The temperature of the gas in the containing vessel fell and that in the originally empty vessel rose by an equal amount. In other words \(\mathrm{dT}\) for the two vessel system is zero. Hence
\[\left(\frac{\partial \mathrm{U}_{j}}{\partial \mathrm{T}}\right)_{\mathrm{V}}=0 \nonumber \]
The clear hope was that the temperature would fall dramatically leading to liquefaction of the gas. In fact and with the benefit of hindsight the overall change in temperature \(\mathrm{dT}\) was too small to be measured. More sophisticated apparatus would show that \(\left(\frac{\partial \mathrm{U}_{\mathrm{j}}}{\partial \mathrm{T}}\right)_{\mathrm{V}} \neq 0\) because as the gas expands work is done against cohesive intermolecular interaction. It would only be zero for a perfect gas.
Experiments by Joule and Thomson [2,3]
In a series of famous experiments carried out in an English brewery, Joule and Thomson used an apparatus in which the gas under study passed through a porous plug from high to low pressures. The plug impeded the flow of the gas such that the pressure of the gas on the high pressure side and the pressure of gas on the low pressure side remained constant. It was observed that the temperature of the gas decreased as a consequence of the work done by the gas against intermolecular cohesion.
A technological breakthrough was now made. A portion of the cooled gas was re-cycled to cool the gas on the input side. On passing through the plug the temperature of the gas fell to a lower temperature. As this process continues a stage was reached where a fraction of the gas is liquefied.
As noted above, the cooling emerges because work is done on expansion of the gases against intermolecular interaction. This is a quite general observation. When the pressure drops the mean intermolecular distance increases with the result that the temperature decreases. However there are exceptions to this generalisation. If the pressure is high the dominant intermolecular force is repulsion. Consequently when the pressure drops, work is done by the repulsive forces increasing the intermolecular distances thereby raising the temperature.
Footnotes
[1] The account given here is based on that given by N. K. Adam, Physical Chemistry, Oxford, The Clarendon Press, 1956, chapter III.
[2] Thomson ≡ Lord Kelvin
[3] J. P. Joule and W. Thomson, Proc. Roy. Soc.,1853, 143 ,3457.
[4] G.N. Lewis and M. Randall, Thermodynamics, revised by K. S. Pitzer and L Brewer, McGraw-Hill, 2nd. edn.,1961, New York, pages 47-49.


29: Are Batman and Superman the Barometer of Our Times? A Review of ‘Superheroes in Crisis’ (Franco)
Ira Erika Franco
#heroes #review #artsandculture, #analysis, #scholarly, #informative
Abstract
The WWII historian Jeffrey K. Johnson studies how the two comic book legends Superman and Batman have adapted successfully to American cultural and social landscapes through time. This is a book review of ‘Superheroes in Crisis’, a monograph that details some decisive moments from their creation in the late 30’s up to the 70’s in which both characters have transformed in order to maintain their relevance as what Johnson calls ‘cultural barometers’.
Keywords: superheroes , history , batman , superman , monographs
The idea that superhero comic books are part of a modern American mythology is probably not a surprise to anyone. However, Jeffrey Johnson refocuses this concept in his monograph Superheroes in Crisis ( RIT Press, 2014 ): after going into detail of the myriad of changes Superman and Batman have gone to stay relevant, he suggests we should narrow our assumptions of what constitutes a true comic book myth, given that the character stays true to what the present society demands. ‘American culture is littered with faint remembrances of characters who flourished for a season and then became inconsequential and vanished’ ( Johnson 2014: 104 ). The author mentions The Yellow Kid and Captain Marvel as those characters who were once ü ber famous and popular and now are but receding memories in people’s minds. Avid comic readers can surely think of many other examples of great modern characters who, for some reason, just didn’t make it. Batman and Superman, however, remain ‘two heroes who have survived, and often thrived, for over seventy years because they are important to current Americans and speak to modern social problems and contemporary cultural necessities’ ( Johnson 2014: 104 ).
A noted World War II historian, Johnson points out that the characters have endured the trials of time mainly because of their abilities to bend so as not to break. Even if most of us modern readers assume fixed traits for both The Dark Knight and The Man of Steel, Johnson carefully demonstrates there’s no such thing: Superman couldn’t even fly in his earliest adventures, and through the period of the TV series in the mid-sixties, Batman, the so-called Dark Knight, was a goofy, campy character with not a bit of darkness in his soul. Through Johnson’s account it is evident, though, that Batman and his creators have done a better job than Superman’s in adjusting to radical changes in American society (such as the US’s disillusionment after JFK’s assassination or the introduction of TV and its immediate popularity). This might also be the reason for Batman’s smoother translation to modern cinema: since the release of the first movie — Batman ( Burton, 1989 )— has always kept the public interest with strong sales figures, — The Dark Knight ( Nolan, 2008 ) being the most popular to date, having made 533 million dollars in revenue for its creators in the US alone —. Not even the bad Batman movies have flopped in opening weekends: people always want to see The Dark Knight’s new metamorphosis, as if they wanted to understand what they’ve turned into.
In the four chapters of the book, Johnson provides the reader with the rare pleasure of being told old stories, gems actually: instead of just sociological analysis and high ideas, Johnson provides the actual plot of the comic issue he chooses in order to support his commentary. We might remember that Superman was created during the Great Depression (1938), and it’s fairly easy to assume that the caped hero was to provide a temporary escape for impoverished and desperate Americans, but unless we have an infinite (and expensive) golden age collection, it would probably never occur to us that during his first few years, Superman was actually a savior of the oppressed, almost in a Marxist fashion. One example is Action Comics #3, where Superman disguises himself as a coal miner to trap the mine owner and his socialite friends underground in order to show them the importance of safety regulations and working men.  In the end, Superman becomes a true hero: he forces the government to build new apartments providing these hooligans the dignity they deserve. Throughout the book, Johnson provides such examples in effective ways to prove the Historic turmoil to which our heroes reacted.
One compelling topic that defines both characters concerns their enemies. At first, being created as depression-era social avengers, they fight the common criminal: shoplifters, wife-beaters and even politicians. ‘These often colorful foes provided action and adventure while also creating a binary narrative of good and evil’ ( Johnson 2014, XIV ). But this narrative changes greatly throughout time, constituting probably the most important transformation in the stories of these two heroes: the evolution of their foes. At some point, the duality of pure good and evil stops being good enough. It stops explaining what is wrong with the world. At the end of the sixties, for example, Superman’s petty villains become so unimportant that, for a while, his love interest Lois Lane impersonates a new kind of foe. In a way, Lois updates better than Superman as she wakes up to her newfound power, akin to the zeitgeist of her era. In Lois Lane #85 (she even gets her own title for a little while) the one-time docile girlfriend decides she no longer wants to marry Superman and refuses his once longed-for offer. In a kind of confused, first approach feminism, she is seen doing things such as lifting heavy stuff like men. ‘Superman represents the older generations and is pressing to protect the status quo, while Lois is a change-minded baby boomer’ ( Johnson 2014: 43 ).
Image 1
Superman’s Girlfriend, Lois Lane Vol 1 #80, Curt Swan, Leo Dorfman, DC Comics, January, 1968. Image via Wikia, DC Comics Database, http://dc.wikia.com/wiki/Superman ’s_Girlfriend,_Lois_Lane_Vol_1_80 . © DC Comics.
Batman’s enemies are, without a doubt, the most exciting ones. First of all, he gets one in the real world: he is accused of promoting homosexuality by the psychologist Frederic Werthan, in his book Seduction of the Innocent ( 1954 ), for which Americans changed the regulation code of the comic book industry. Later, in the early sixties, the character is handed to writer and editor Julius Schwartz and the stories become enriched with a focus on Batman’s detective skills. The Riddler, Mr. Freeze and the Joker all demand The Caped Crusader’s brainpower to discover complex noir plots, creating a three-dimensional world within the comic’s pages: ‘Perhaps most interesting is Detective Comics#332 (October 1964) in which Batman fights Joker for the first time under the new creative regime. In this story the Clown Prince of Crime creates a potent dust that causes anyone it comes in contact with to laugh uncontrollably. After encountering the drug, Batman researches possible cures and learns that a simple antihistamine will stop the uncontainable laughter. The Caped Crusader soon thwarts the villain’s evil plans and protects society from the psychopathic clown. This version of Batman is portrayed as being clearly more intelligent and cunning than his arch-nemesis, but The Joker is also more nefarious and crafty than he had been in recent appearances’. ( Johnson 2014, 36 ). It is only natural to think that Batman’s foes evolve in complexity over time, the greatest example being a villain like Ra’s al Ghul, who, defying normal stereotyping, commits awful crimes believing it is best for the planet.
In this constant reshaping of the characters, one thing remains constant from the beginning: the foes are more metaphorical than the heroes for the darkest fears of American society in the way they reflect the heroes’ moral codes. In the first chapter, for example, that covers the early years (from 1938 to 1959), most evildoers evoke the desperate need of common people to keep America’s status quo. Superman fights against gamblers taking control over football games and ‘declares war on reckless drivers’.  ‘These first superheroes were violent champions for a hardened people who demanded they act in such a way. The original versions of Superman and Batman did not conform to the rules against killing, maiming, battling authority figures and law enforcement’ ( Johnson 2014: XVII ). Johnson thinks these initial times can be seen, especially in Superman, as a kind of an adolescence because of his disregard for any point of view except his own. More a bully than a hero, Superman reflects the state of millions of Americans, adult men out of work ‘who had descended into hopelessness and Superman served as a bright spot in this bleak depressing age’ ( Johnson 2014: 2 ).
Just three years later, with the entry of the US to World War II, the nature of both criminals and heroes changed radically: both Batman and Superman had to support governmental and military mandates, slowly becoming in the years to come guardians of the conventional values that were established with the prosperity and the sense of social unity that came after the victory over the Axis armies. What happened to our heroes in the sixties reflected a harsh division in the American people: while Superman becomes almost infected with paranoia and self-righteousness that characterized the conservatives in the post war era —having nightmares of being exposed to red kryptonite, splitting into evil Superman and good Clark Kent, turning into a space monster, among other adventures—, Batman goes through some nice years of detectivesque narrative, preparing for the blossoming of sexual liberation and anti-war movements that would become popular among youngsters a few years later. ‘The Dark Knight was now focusing more on his detective skills and was no longer fighting aliens or magical beings as he had in previous years…Batman was attempting to recreate himself from an evolving society, but it was unclear if a return to his detective roots combined with pop art influences was what readers demanded’ ( Johnson 2014: 35 ).
One last thing is to note of this book: the detailed attention Johnson pays to the creative minds that shaped these heroes. Bob Kane may have designed Batman to be a ‘hardcore vigilante’, but it was Julius Schwartz in 1964 who invented some of his most engaging traits as a resourceful hard-boiled detective with no other tools to fight crime but his mind. Writers and artists like Frank Robbins, Bob Brown and Dick Giordano are mentioned as inventive, but Johnson points out a very short but fertile period in the seventies that would prepare the dark and gothic traits of Batman we have come to love, under the hands of writer Denny O’Neal and artist Neal Adams. In this period Batman first gets his many layers as a character, his neurosis and most subtle psychological features that Frank Miller would use in his ground-breaking The Dark Knight Returns (1986), later revamped for Christopher Nolan’s Dark Knight’s Trilogy.
Above all, the great journey this book offers is discovering how our beloved heroes appear to be two ends of the same rope, because, paradoxically, even when they change, they stay the same: Superman representing (mostly) the moral standards of the conservative side of American society, and Batman exploring (mostly) the darker, subterranean side, both equally sustaining and fundamental to the American social fabric.
References
- Batman (1989). Burton, Tim Warner Bros.
- Johnson, JK (2014). Superheroes in Crisis: Adjusting to Social Change in the 1960s and 1970s . RIT Press. 122
- The Dark Knight (). Trilogy is a film series directed by Christopher Nolan. It consists In: Batman Begins (2005), The Dark Knight (2008) and The Dark Knight Rises (2012) . Warner Bros Pictures.
- Werthan, Frederic . (1954). Seduction of the Innocent In: New York Reinhart & Co.. 400
____________________
Ira Erika Franco is is a teacher in Communication for the National Autonomous University of Mexico . She is a film director, a travel writer, and a film and theater critic. Her work appears in Chilango and Muy Interesante . This review is reprinted from The Comics Grid .
Are Batman and Superman the Barometer of Our Times? A Review of ‘Superheroes in Crisis’ by Ira Erika Franco is licensed under a Creative Commons Attribution 3.0 International License .