1.3: Glance at Critical Response- Rhetoric and Critical Thinking
By the end of this section, you will be able to:
- Use words, images, and specific rhetorical terminology to understand, discuss, and analyze a variety of texts.
- Determine how genre conventions are shaped by audience, purpose, language, culture, and expectation.
- Distinguish among different types of rhetorical situations and communicate effectively within them.
Every day you find yourself in rhetorical situations and use rhetoric to communicate with and to persuade others, even though you might not realize you are doing it.
For example, when you voice your opinion or respond to another’s opinion, you are thinking rhetorically. Your purpose is often to convince others that you have a valid opinion, and maybe even issue a call to action. Obviously, you use words to communicate and present your position. But you may communicate effectively through images as well.
Words and Images
Both words and images convey information, but each does so in significantly different ways. In English, words are written sequentially, from left to right. A look at a daily newspaper or web page reveals textual information further augmented by headlines, titles, subtitles, boldface, italics, white space, and images. By the time readers get to college, they have internalized predictive strategies to help them critically understand a variety of written texts and the images that accompany them. For example, you might be able to predict the words in a sentence as you are reading it. You also know the purpose of headers and other markers that guide you through the reading.
To be a critical reader, though, you need to be more than a good predictor. In addition to following the thread of communication, you need to evaluate its logic. To do that, you need to ask questions such as these as you consider the argument: Is it fair (i.e., unbiased)? Does it provide credible evidence? Does it make sense, or is it reasonably plausible? Then, based on what you have decided, you can accept or reject its conclusions. You may also consider alternative possibilities so that you can learn more. In this way, you read actively, searching for information and ideas that you understand and can use to further your own thinking, writing, and speaking. To move from understanding to critical awareness, plan to read a text more than once and in more than one way. One good strategy is to ask questions of a text rather than to accept the author’s ideas as fact. Another strategy is to take notes about your understanding of the passage. And another is to make connections between concepts in different parts of a reading. Maybe an idea on page 4 is reiterated on page 18. To be an active, engaged reader, you will need to build bridges that illustrate how concepts become part of a larger argument. Part of being a good reader is the act of building information bridges within a text and across all the related information you encounter, including your experiences.
With this goal in mind, beware of passive reading. If you ever have been reading and completed a page or paragraph and realized you have little idea of what you’ve just read, you have been reading passively or just moving your eyes across the page. Although you might be able to claim you “read” the material, you have not engaged with the text to learn from it, which is the point of reading. You haven’t built bridges that connect to other material. Remember, words help you make sense of the world, communicate in the world, and create a record to reflect on so that you can build bridges across the information you encounter.
Images, however, present a different set of problems for critical readers. Sometimes having little or no accompanying text, images require a different skill set. For example, in looking at a photograph or drawing, you find different information presented simultaneously. This presentation allows you to scan or stop anywhere in the image—at least theoretically. Because visual information is presented simultaneously, its general meaning may be apparent at a glance, while more nuanced or complicated meanings may take a long time to figure out. And even then, odds are these meanings will vary from one viewer to another.
Figure \(1.3\) Young woman looking away from the viewer or old woman in profile? (credit: "My wife and my mother-in-law" by W.E. (William Ely) Hill/Public Domain)
In the well-known image shown in Figure \(1.3\), do you see an old woman or a young woman? Although the image remains static, your interpretation of it may change depending on any number of factors, including your experience, culture, and education. Once you become aware of the two perspectives of this image, you can see the “other” easily. But if you are not told about the two ways to “see” it, you might defend a perspective without realizing that you are missing another one. Most visuals, however, are not optical illusions; less noticeable perspectives may require more analysis and may be more influenced by your cultural identity and the ways in which you are accustomed to interpreting. In any case, this image is a reminder to have an open mind and be willing to challenge your perspectives against your interpretations. As such, like written communication, images require analysis before they can be understood thoroughly and evaluation before they can be judged on a wider scale.
If you have experience with social media, you may be familiar with the way users respond to images or words by introducing another image: the meme .
A meme is a photograph containing text that presents one viewer’s response. The term meme originates from the Greek root mim , meaning “mime” or “mimic,” and the English suffix -eme . In the 1970s, British evolutionary biologist and author Richard Dawkins (b. 1941) created the term for use as “a unit of cultural transmission,” and he understood it to be “the cultural equivalent of a gene.” Today, according to the dictionary definition, memes are “amusing or interesting items that spread widely through the Internet.” For example, maybe you have seen a meme of an upset cat or of a friend turning around to look at something else while another friend is relating something important. The text that accompanies these pictures provides some expression on the part of the originator that the audience usually finds humorous, relatable, or capable of arousing any range of emotion or thought. For example, in the photograph shown in Figure \(1.4\) of a critter standing at attention, the author of the text conveys anxiousness. The use of the word like has been popularized in the meme genre to mean “to give an example.”
Figure \(1.4\) Example of a meme (credit: "Waiting for you like . . ." by Marco Verch/flickr/CC BY 2.0)
While these playful aspects of images are important, you also should recognize how images fit into the rhetorical situation. Consider the same elements, such as context and genre, when viewing images. You may find multiple perspectives to consider. In addition, where images show up in a text or for an audience might be important. These are all aspects of understanding the situation and thinking critically. Engaged readers try to connect and build bridges to information across text and images.
As you consider your reading and viewing experiences on social media and elsewhere, note that your responses involve some basic critical thinking strategies. Some of these include summary, paraphrase, analysis, and evaluation, which are defined in the next section. The remaining parts of this chapter will focus on written communication. While this chapter touches only briefly on visual discourse, Image Analysis: What You See presents an extensive discussion on visual communication.
Relation to Academics
As with all disciplines, rhetoric has its own vocabulary. What follows are key terms, definitions, and elements of rhetoric. Become familiar with them as you discuss and write responses to the various texts and images you will encounter.
- Analysis: detailed breakdown or other explanation of some aspect or aspects of a text. Analysis helps readers understand the meaning of a text.
- Authority: credibility; background that reflects experience, knowledge, or understanding of a situation. An authoritative voice is clear, direct, factual, and specific, leaving an impression of confidence.
- Context: setting—time and place—of the rhetorical situation. The context affects the ways in which a particular social, political, or economic situation influences the process of communication. Depending on context, you may need to adapt your text to audience background and knowledge by supplying (or omitting) information, clarifying terminology, or using language that best reaches your readers.
- Culture: group of people who share common beliefs and lived experiences. Each person belongs to various cultures, such as a workplace, school, sports team fan, or community.
- Evaluation: systematic assessment and judgment based on specific and articulated criteria, with a goal to improve understanding.
- Evidence: support or proof for a fact, opinion, or statement. Evidence can be presented as statistics, examples, expert opinions, analogies, case studies, text quotations, research in the field, videos, interviews, and other sources of credible information.
- Media literacy: ability to create, understand, and evaluate various types of media; more specifically, the ability to apply critical thinking skills to them.
- Meme: image (usually) with accompanying text that calls for a response or elicits a reaction.
- Paraphrase: rewording of original text to make it clearer for readers. When they are part of your text, paraphrases require a citation of the original source.
- Rhetoric: use of effective communication in written, visual, or other forms and understanding of its impact on audiences as well as of its organization and structure.
- Rhetorical situation: instance of communication; the conditions of a communication and the agents of that communication.
- Social media: all digital tools that allow individuals or groups to create, post, share, or otherwise express themselves in a public forum. Social media platforms publish instantly and can reach a wide audience.
- Summary: condensed account of a text or other form of communication, noting its main points. Summaries are written in one’s own words and require appropriate attribution when used as part of a paper.
- Tone: an author’s projected or perceived attitude toward the subject matter and audience. Word choice, vocal inflection, pacing, and other stylistic choices may make the author sound angry, sarcastic, apologetic, resigned, uncertain, authoritative, and so on.
As you read through these terms, you likely recognize most of them and realize you are adept in some rhetorical situations. For example, when you talk with friends about your trip to the local mall, you provide details they will understand. You might refer to previous trips or tell them what is on sale or that you expect to see someone from school there. In other words, you understand the components of the rhetorical situation. However, if you tell your grandparents about the same trip, the rhetorical situation will be different, and you will approach the interaction differently. Because the audience is different, you likely will explain the event with more detail to address the fact that they don’t go to the mall often, or you will omit specific details that your grandparents will not understand or find interesting. For instance, instead of telling them about the video game store, you might tell them about the pretzel café.
As part of your understanding of the rhetorical situation, you might summarize specific elements, again depending on the intended audience. You might speak briefly about the pretzel café to your friends but spend more time detailing the various toppings for your grandparents. If, by chance, you have previously stopped to have a pretzel, you might provide your analysis and evaluation of the service and the food. Once again, you are engaged in rhetoric by showing an understanding of and the ability to develop a strategy for approaching a particular rhetorical situation. The point is to recognize that rhetorical situations differ, depending, in this case, on the audience. Awareness of the rhetorical situation applies to academic writing as well. You change your presentation, tone, style, and other elements to fit the conditions of the situation.


7.E: The Central Limit Theorem (Exercises)
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These are homework exercises to accompany the Textmap created for
"Introductory Statistics" by OpenStax.
7.1: Introduction
7.2: The Central Limit Theorem for Sample Means (Averages)
Q 7.2.1
Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.
- In words, \(Χ =\) ____________
- \(Χ \sim\) _____(_____,_____)
- In words, \(\bar{X} =\) ____________
- \(\bar{X} \sim\) ______ (______, ______)
- Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
- Find the probability that the average of the 25 students was between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
- Explain why there is a difference in part e and part f.
S 7.2.1
- \(Χ =\) amount of change students carry
- \(Χ \sim E(0.88, 0.88)\)
- \(\bar{X} =\) average amount of change carried by a sample of 25 students.
- \(\bar{X} \sim N(0.88, 0.176)\)
- 0.0819
- 0.1882
- The distributions are different. Part a is exponential and part b is normal.
Q 7.2.2
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
- If \(\bar{X} =\) average distance in feet for 49 fly balls, then \(\bar{X} \sim\) _______(_______,_______)
- What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for \(\bar{X}\). Shade the region corresponding to the probability. Find the probability.
- Find the 80 th percentile of the distribution of the average of 49 fly balls.
Q 7.2.3
According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers.
- In words, \(Χ =\) _____________
- In words, \(\bar{X} =\) _____________
- \(\bar{X} \sim\) _____(_____,_____)
- Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences.
- Would you be surprised if one taxpayer finished his or her Form 1040 in more than 12 hours? In a complete sentence, explain why.
S 7.2.3
- length of time for an individual to complete IRS form 1040, in hours.
- mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours.
- \(N\left(10.53, \frac{1}{3}\right)\)
- Yes. I would be surprised, because the probability is almost 0.
- No. I would not be totally surprised because the probability is 0.2312
Q 7.2.4
Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let \(\bar{X}\) the average of the 49 races.
- \(\bar{X} \sim\) _____(_____,_____)
- Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.
- Find the 80 th percentile for the average of these 49 marathons.
- Find the median of the average running times.
Q 7.2.5
The length of songs in a collector’s iTunes album collection is uniformly distributed from two to 3.5 minutes. Suppose we randomly pick five albums from the collection. There are a total of 43 songs on the five albums.
- In words, \(Χ =\) _________
- \(\bar{X} \sim\) _____________
- In words, \(\bar{X} =\) _____________
- \(\bar{X} \sim\) _____(_____,_____)
- Find the first quartile for the average song length.
- The IQR(interquartile range) for the average song length is from _______–_______.
S 7.2.6
- the length of a song, in minutes, in the collection
- \(U(2, 3.5)\)
- the average length, in minutes, of the songs from a sample of five albums from the collection
- \(N(2.75, 0.0220)\)
- 2.74 minutes
- 0.03 minutes
Q 7.2.7
In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940.
- In words, \(Χ =\) _____________
- In words, \(\bar{X} =\) _____________
- \(\bar{X} \sim\) _____(_____,_____)
- The IQR for \(\bar{X}\) is from _______ acres to _______ acres.
Q 7.2.8
Determine which of the following are true and which are false.
- When the sample size is large, the mean of \(\bar{X}\) is approximately equal to the mean of \(Χ\).
- When the sample size is large, \(\bar{X}\) is approximately normally distributed.
- When the sample size is large, the standard deviation of \(\bar{X}\) is approximately the same as the standard deviation of \(Χ\).
S 7.2.8
- True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
- True. According to the Central Limit Theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
- The standard deviation of the sampling distribution of the means will decrease making it approximately the same as the standard deviation of \(Χ\) as the sample size increases.
Q 7.2.9
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. Let \(\bar{X} =\) average percent of fat calories.
- \(\bar{X} \sim\) ______(______, ______)
- For the group of 16, find the probability that the average percent of fat calories consumed is more than five. Graph the situation and shade in the area to be determined.
- Find the first quartile for the average percent of fat calories.
Q 7.2.10
The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be $2,000 per year with a standard deviation of $8,000. We randomly survey 1,000 residents of that country.
- In words, \(Χ =\) _____________
- In words, \(\bar{X} =\) _____________
- \(\bar{X} \sim\) _____(_____,_____)
- How is it possible for the standard deviation to be greater than the average?
- Why is it more likely that the average of the 1,000 residents will be from $2,000 to $2,100 than from $2,100 to $2,200?
S 7.2.10
- \(Χ =\) the yearly income of someone in a third world country
- the average salary from samples of 1,000 residents of a third world country
- \(\bar{X} \sim N\left(2000, \frac{8000}{\sqrt{1000}}\right)\)
- Very wide differences in data values can have averages smaller than standard deviations.
-
The distribution of the sample mean will have higher probabilities closer to the population mean.
\(P(2000 < \bar{X} < 2100) = 0.1537\)
\(P(2100 < \bar{X} < 2200) = 0.1317\)
Q 7.2.11
Which of the following is NOT TRUE about the distribution for averages?
- The mean, median, and mode are equal.
- The area under the curve is one.
- The curve never touches the x -axis.
- The curve is skewed to the right.
Q 7.2.12
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. The distribution to use for the average cost of gasoline for the 16 gas stations is:
- \(\bar{X} \sim N(4.59, 0.10)\)
- \(\bar{X} \sim N\left(4.59, \frac{0.10}{\sqrt{16}}\right)\)
- \(\bar{X} \sim N\left(4.59, \frac{16}{0.10}\right)\)
- \(\bar{X} \sim N\left(4.59, \frac{\sqrt{16}}{0.10}\right)\)
S 7.2.12
b
7.3: The Central Limit Theorem for Sums
Q 7.3.1
Which of the following is NOT TRUE about the theoretical distribution of sums?
- The mean, median and mode are equal.
- The area under the curve is one.
- The curve never touches the x -axis.
- The curve is skewed to the right.
Q 7.3.2
Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of seven days. We randomly sample nine trials.
- In words, \(\sum X =\) ______________
- \(\sum X \sim\) _____(_____,_____)
- Find the probability that the total length of the nine trials is at least 225 days.
- Ninety percent of the total of nine of these types of trials will last at least how long?
S 7.3.2
- the total length of time for nine criminal trials
- \(N(189, 21)\)
- 0.0432
- 162.09; ninety percent of the total nine trials of this type will last 162 days or more.
Q 7.3.3
Suppose that the weight of open boxes of cereal in a home with children is uniformly distributed from two to six pounds with a mean of four pounds and standard deviation of 1.1547. We randomly survey 64 homes with children.
- In words, \(X =\)_____________
- The distribution is _______.
- In words, \(\sum X =\) _______________
- \(\sum X \sim\) _____(_____,_____)
- Find the probability that the total weight of open boxes is less than 250 pounds.
- Find the 35 th percentile for the total weight of open boxes of cereal.
Q 7.3.4
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district.
- In words, \(X =\) ______________
- \(X \sim\) _____(_____,_____)
- In words, \(\sum X =\) _____________
- \(\sum X \sim\) _____(_____,_____)
- Find the probability that the teachers earn a total of over $400,000.
- Find the 90 th percentile for an individual teacher's salary.
- Find the 90 th percentile for the sum of ten teachers' salary.
- If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part d?
- If each of the 70 teachers received a $3,000 raise, graphically, how would that change the distribution in part b?
S 7.3.4
- \(X =\) the salary of one elementary school teacher in the district
- \(X \sim N(44,000, 6,500)\)
- \(\sum X \sim\) sum of the salaries of ten elementary school teachers in the sample
- \(\sum X \sim N(44000, 20554.80)\)
- 0.9742
- $52,330.09
- 466,342.04
- Sampling 70 teachers instead of ten would cause the distribution to be more spread out. It would be a more symmetrical normal curve.
- If every teacher received a $3,000 raise, the distribution of X would shift to the right by $3,000. In other words, it would have a mean of $47,000.
Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.
Exercise 7.3.4
Find the probability that the sum of the 95 values is greater than 7,650.
Answer
0.3345
Exercise 7.3.5
Find the probability that the sum of the 95 values is less than 7,400.
Exercise 7.3.6
Find the sum that is two standard deviations above the mean of the sums.
Answer
7,833.92
Exercise 7.3.7
Find the sum that is 1.5 standard deviations below the mean of the sums.
Use the following information to answer the next five exercises: The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.
Exercise 7.3.8
Find the probability that the sum of the 40 values is greater than 7,500.
Answer
0.0089
Exercise 7.3.9
Find the probability that the sum of the 40 values is less than 7,000.
Exercise 7.3.10
Find the sum that is one standard deviation above the mean of the sums.
Answer
7,326.49
Exercise 7.3.11
Find the sum that is 1.5 standard deviations below the mean of the sums.
Exercise 7.3.12
Find the percentage of sums between 1.5 standard deviations below the mean of the sums and one standard deviation above the mean of the sums.
Answer
77.45%
Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100.
Exercise 7.3.13
Find the probability that the sum of the 100 values is greater than 3,910.
Exercise 7.3.14
Find the probability that the sum of the 100 values is less than 3,900.
Answer
0.4207
Exercise 7.3.15
Find the probability that the sum of the 100 values falls between the numbers you found in Problem and Problem .
Exercise 7.3.16
Find the sum with a \(z\) - score of –2.5.
Answer
3,888.5
Exercise 7.3.17
Find the sum with a z –score of 0.5.
Exercise 7.3.18
Find the probability that the sums will fall between the \(z\)-scores –2 and 1.
Answer
0.8186
Use the following information to answer the next four exercise: An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let \(X\) = the object of interest.
Exercise 7.3.19
What is the mean of \(\sum X\)?
Exercise 7.3.20
What is the standard deviation of \(\sum X\)?
Answer
5
Exercise 7.3.21
What is \(P(\sum x = 290)\)?
Exercise 7.3.22
What is \(P(\sum x > 290)\)?
Answer
0.9772
Exercise 7.3.23
True or False: only the sums of normal distributions are also normal distributions.
Exercise 7.3.24
In order for the sums of a distribution to approach a normal distribution, what must be true?
Answer
The sample size, \(n\), gets larger.
Exercise 7.3.25
What three things must you know about a distribution to find the probability of sums?
Exercise 7.3.26
An unknown distribution has a mean of 25 and a standard deviation of six. Let \(X\) = one object from this distribution. What is the sample size if the standard deviation of \(\sum X\) is 42?
Answer
49
Exercise 7.3.27
An unknown distribution has a mean of 19 and a standard deviation of 20. Let \(X\) = the object of interest. What is the sample size if the mean of \(\sum X\) is 15,200?
Use the following information to answer the next three exercises. A market researcher analyzes how many electronics devices customers buy in a single purchase. The distribution has a mean of three with a standard deviation of 0.7. She samples 400 customers.
Exercise 7.3.28
What is the \(z\)-score for \(\sum x = 840\)?
Answer
26.00
Exercise 7.3.29
What is the \(z\)-score for \(\sum x = 1,186\)?
Exercise 7.3.30
What is \(P(\sum x < 1,186)\)?
Answer
0.1587
Use the following information to answer the next three exercises: An unknown distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let \(X\) = one object of interest.
Exercise 7.3.31
What is the mean of \(\sum X\)?
Exercise 7.3.32
What is the standard deviation of \(\sum X\)?
Answer
1,000
Exercise 7.3.33
What is \(P(\sum x > 9,000)\)?
7.4: Using th Central Limit Theorem
Q 7.4.1
The attention span of a two-year-old is exponentially distributed with a mean of about eight minutes. Suppose we randomly survey 60 two-year-olds.
- In words, \(X =\) _______
- \(X \sim\) _____(_____,_____)
- In words, \(\sum X =\) ____________
- \(\sum X \sim\) _____(_____,_____)
-
Before doing any calculations, which do you think will be higher? Explain why.
- The probability that an individual attention span is less than ten minutes.
- The probability that the average attention span for the 60 children is less than ten minutes?
- Calculate the probabilities in part e.
- Explain why the distribution for \(\bar{X}\) is not exponential.
Q 7.4.2
The closing stock prices of 35 U.S. semiconductor manufacturers are given as follows.
8.625, 30.25, 27.625, 46.75, 32.875, 18.25, 5, 0.125, 2.9375, 6.875, 28.25, 24.25, 21, 1.5, 30.25, 71, 43.5, 49.25, 2.5625, 31, 16.5, 9.5, 18.5, 18, 9, 10.5, 16.625, 1.25, 18, 12.87, 7, 12.875, 2.875, 60.25, 29.25
- In words, \(Χ =\) ______________
-
- \(\bar{X} =\) _____
- \(s_{X} =\) _____
- \(n =\) _____
- Construct a histogram of the distribution of the averages. Start at x = –0.0005. Use bar widths of ten.
- In words, describe the distribution of stock prices.
- Randomly average five stock prices together. (Use a random number generator.) Continue averaging five pieces together until you have ten averages. List those ten averages.
-
Use the ten averages from part e to calculate the following.
- \(\bar{X} =\) _____
- \(s_{X} =\) _____
- Construct a histogram of the distribution of the averages. Start at x = -0.0005. Use bar widths of ten.
- Does this histogram look like the graph in part c?
- In one or two complete sentences, explain why the graphs either look the same or look different?
- Based upon the theory of the central limit theorem , \(\bar{X} \sim\) _____(_____,____)
S 7.4.2
- \(X =\) the closing stock prices for U.S. semiconductor manufacturers
- i. $20.71; ii. $17.31; iii. 35
- Exponential distribution, \(Χ \sim \text{Exp}\left(\frac{1}{20.71}\right)\)
- Answers will vary.
- i. $20.71; ii. $11.14
- Answers will vary.
- Answers will vary.
- Answers will vary.
- \(N\left(20.71, \frac{17.31}{\sqrt{5}}\right)\)
Use the following information to answer the next three exercises: Richard’s Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested in how long (in hours) past the 10 A.M. start time that individuals wait for their delivery.
Q 7.4.3
\(Χ \sim\) _____(_____,_____)
- \(U(0,4)\)
- \(U(10,2)\)
- \(Exp(2)\)
- \(N(2,1)\)
Q 7.4.4
The average wait time is:
- one hour.
- two hours.
- two and a half hours.
- four hours.
S 7.4.4
b
Q 7.4.5
Suppose that it is now past noon on a delivery day. The probability that a person must wait at least one and a half more hours is:
- \(\frac{1}{4}\)
- \(\frac{1}{2}\)
- \(\frac{3}{4}\)
- \(\frac{3}{8}\)
Use the following information to answer the next two exercises: The time to wait for a particular rural bus is distributed uniformly from zero to 75 minutes. One hundred riders are randomly sampled to learn how long they waited.
Q 7.4.6
The 90 th percentile sample average wait time (in minutes) for a sample of 100 riders is:
- 315.0
- 40.3
- 38.5
- 65.2
S 7.4.6
b
Q 7.4.7
Would you be surprised, based upon numerical calculations, if the sample average wait time (in minutes) for 100 riders was less than 30 minutes?
- yes
- no
- There is not enough information.
Use the following to answer the next two exercises: The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations.
Q 7.4.8
What's the approximate probability that the average price for 16 gas stations is over $4.69?
- almost zero
- 0.1587
- 0.0943
- unknown
S 7.4.8
a
Q 7.4.9
Find the probability that the average price for 30 gas stations is less than $4.55.
- 0.6554
- 0.3446
- 0.0142
- 0.9858
- 0
Q 7.4.10
Suppose in a local Kindergarten through 12 th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 300 is surveyed. Calculate following using the normal approximation to the binomial distribution.
- Find the probability that less than 100 favor a charter school for grades K through 5.
- Find the probability that 170 or more favor a charter school for grades K through 5.
- Find the probability that no more than 140 favor a charter school for grades K through 5.
- Find the probability that there are fewer than 130 that favor a charter school for grades K through 5.
- Find the probability that exactly 150 favor a charter school for grades K through 5.
If you have access to an appropriate calculator or computer software, try calculating these probabilities using the technology.
S 7.4.10
- 0
- 0.1123
- 0.0162
- 0.0003
- 0.0268
Q 7.4.11
Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for 96 days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places.
- Find the probability that Janice is the driver at most 20 days.
- Find the probability that Roberta is the driver more than 16 days.
- Find the probability that Barbara drives exactly 24 of those 96 days.
Q 7.4.12
\(X ~ N(60, 9)\). Suppose that you form random samples of 25 from this distribution. Let \(\bar{X}\) be the random variable of averages. Let \(\sum X\) be the random variable of sums. For parts c through f, sketch the graph, shade the region, label and scale the horizontal axis for \(\bar{X}\), and find the probability.
- Sketch the distributions of \(X\) and \(\bar{X}\) on the same graph.
- \(\bar{X} \sim\) _____(_____,_____)
- \(P(\bar{x} < 60) =\) _____
- Find the 30 th percentile for the mean.
- \(P(56 < \bar{x} < 62)\) = _____
- \(P(18 < \bar{x} < 58)\) = _____
- \(\sum X \sim\) _____(_____,_____)
- Find the minimum value for the upper quartile for the sum.
- \(P(1,400 < \sum X < 1,550) =\) _____
S 7.4.12
- Check student’s solution.
- \(\bar{X} \sim N\left(60, 925\right)\)
- 0.5000
- 59.06
- 0.8536
- 0.1333
- \(N(1500, 45)\)
- 1530.35
- 0.6877
Q 7.4.13
Suppose that the length of research papers is uniformly distributed from ten to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.
- In words, \(X =\) _____________
- \(X \sim\) _____(_____,_____)
- \(\mu_{X} =\) _____
- \(\sigma_{X} =\) _____
- In words, \(\bar{X} =\) ______________
- \(\bar{X} \sim\) _____(_____,_____)
- In words, \(\sum X =\) _____________
- \(\sum X\ sim\) _____(_____,_____)
- Without doing any calculations, do you think that it’s likely that the professor will need to read a total of more than 1,050 pages? Why?
- Calculate the probability that the professor will need to read a total of more than 1,050 pages.
- Why is it so unlikely that the average length of the papers will be less than 12 pages?
Q 7.4.14
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district.
- Find the 90 th percentile for an individual teacher’s salary.
- Find the 90 th percentile for the average teacher’s salary.
S 7.4.14
- $52,330
- $46,634
Q 7.4.15
The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.
- In words, \(X =\) _____________
- In words, \(\bar{X} =\) ___________________
- \(\bar{X} \sim\) _____(_____,_____)
- In words, \(\sum X =\) _______________
- \(\sum X \sim\) _____(_____,_____)
- Is it likely that an individual stayed more than five days in the hospital? Why or why not?
- Is it likely that the average stay for the 80 women was more than five days? Why or why not?
-
Which is more likely:
- An individual stayed more than five days.
- the average stay of 80 women was more than five days.
- If we were to sum up the women’s stays, is it likely that, collectively they spent more than a year in the hospital? Why or why not?
For each problem, wherever possible, provide graphs and use the calculator.
Q 7.4.16
NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your statistics class questions this claim. As a class, you randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly, what is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 16.7 hours or less? Is the company’s claim reasonable?
S 7.4.16
-
We have \(\mu = 17, \sigma = 0.8, \bar{x} = 16.7\), and \(n = 30\). To calculate the probability, we use
normalcdf
(lower, upper, \(\mu\), \(\frac{\sigma}{\sqrt{n}}\)) =normalcdf
\(\left(E–99,16.7,17,\frac{0.8}{\sqrt{30}}\right) = 0.0200\). - If the process is working properly, then the probability that a sample of 30 batteries would have at most 16.7 lifetime hours is only 2%. Therefore, the class was justified to question the claim.
Q 7.4.17
Men have an average weight of 172 pounds with a standard deviation of 29 pounds.
- Find the probability that 20 randomly selected men will have a sum weight greater than 3600 lbs.
- If 20 men have a sum weight greater than 3500 lbs, then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.
Q 7.4.18
M&M candies large candy bags have a claimed net weight of 396.9 g. The standard deviation for the weight of the individual candies is 0.017 g. The following table is from a stats experiment conducted by a statistics class.
| Red | Orange | Yellow | Brown | Blue | Green |
|---|---|---|---|---|---|
| 0.751 | 0.735 | 0.883 | 0.696 | 0.881 | 0.925 |
| 0.841 | 0.895 | 0.769 | 0.876 | 0.863 | 0.914 |
| 0.856 | 0.865 | 0.859 | 0.855 | 0.775 | 0.881 |
| 0.799 | 0.864 | 0.784 | 0.806 | 0.854 | 0.865 |
| 0.966 | 0.852 | 0.824 | 0.840 | 0.810 | 0.865 |
| 0.859 | 0.866 | 0.858 | 0.868 | 0.858 | 1.015 |
| 0.857 | 0.859 | 0.848 | 0.859 | 0.818 | 0.876 |
| 0.942 | 0.838 | 0.851 | 0.982 | 0.868 | 0.809 |
| 0.873 | 0.863 | 0.803 | 0.865 | ||
| 0.809 | 0.888 | 0.932 | 0.848 | ||
| 0.890 | 0.925 | 0.842 | 0.940 | ||
| 0.878 | 0.793 | 0.832 | 0.833 | ||
| 0.905 | 0.977 | 0.807 | 0.845 | ||
| 0.850 | 0.841 | 0.852 | |||
| 0.830 | 0.932 | 0.778 | |||
| 0.856 | 0.833 | 0.814 | |||
| 0.842 | 0.881 | 0.791 | |||
| 0.778 | 0.818 | 0.810 | |||
| 0.786 | 0.864 | 0.881 | |||
| 0.853 | 0.825 | ||||
| 0.864 | 0.855 | ||||
| 0.873 | 0.942 | ||||
| 0.880 | 0.825 | ||||
| 0.882 | 0.869 | ||||
| 0.931 | 0.912 | ||||
| 0.887 |
The bag contained 465 candies and he listed weights in the table came from randomly selected candies. Count the weights.
- Find the mean sample weight and the standard deviation of the sample weights of candies in the table.
- Find the sum of the sample weights in the table and the standard deviation of the sum the of the weights.
- If 465 M&Ms are randomly selected, find the probability that their weights sum to at least 396.9.
- Is the Mars Company’s M&M labeling accurate?
S7.4.19
- For the sample, we have \(n = 100, \bar{x} = 0.862, s = 0.05\)
- \(\sum \bar{x} = 85.65, \sum s = 5.18\)
-
normalcdf
\((396.9,E99,(465)(0.8565),(0.05)\left(\sqrt{465}\right)) \approx 1\) - Since the probability of a sample of size 465 having at least a mean sum of 396.9 is approximately 1, we can conclude that Mars is correctly labeling their M&M packages.
Q7.4.20
The Screw Right Company claims their \(\frac{3}{4}\) inch screws are within \(\pm 0.23\) of the claimed mean diameter of 0.750 inches with a standard deviation of 0.115 inches. The following data were recorded.
| 0.757 | 0.723 | 0.754 | 0.737 | 0.757 | 0.741 | 0.722 | 0.741 | 0.743 | 0.742 |
| 0.740 | 0.758 | 0.724 | 0.739 | 0.736 | 0.735 | 0.760 | 0.750 | 0.759 | 0.754 |
| 0.744 | 0.758 | 0.765 | 0.756 | 0.738 | 0.742 | 0.758 | 0.757 | 0.724 | 0.757 |
| 0.744 | 0.738 | 0.763 | 0.756 | 0.760 | 0.768 | 0.761 | 0.742 | 0.734 | 0.754 |
| 0.758 | 0.735 | 0.740 | 0.743 | 0.737 | 0.737 | 0.725 | 0.761 | 0.758 | 0.756 |
The screws were randomly selected from the local home repair store.
- Find the mean diameter and standard deviation for the sample
- Find the probability that 50 randomly selected screws will be within the stated tolerance levels. Is the company’s diameter claim plausible?
Q 7.4.21
Your company has a contract to perform preventive maintenance on thousands of air-conditioners in a large city. Based on service records from previous years, the time that a technician spends servicing a unit averages one hour with a standard deviation of one hour. In the coming week, your company will service a simple random sample of 70 units in the city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time?
Q 7.4.22
Use
normalcdf
\[(E–99,1.1,1,\frac{1}{\sqrt{70}}) = 0.7986.\]
This means that there is an 80% chance that the service time will be less than 1.1 hours. It could be wise to schedule more time since there is an associated 20% chance that the maintenance time will be greater than 1.1 hours.
Q 7.4.23
A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?
Q 7.4.24
Certain coins have an average weight of 5.201 grams with a standard deviation of 0.065 g. If a vending machine is designed to accept coins whose weights range from 5.111 g to 5.291 g, what is the expected number of rejected coins when 280 randomly selected coins are inserted into the machine?
S 7.4.25
Since we have
normalcdf
\((5.111,5.291,5.201,\frac{0.065}{\sqrt{280}}) \approx 1\), we can conclude that practically all the coins are within the limits, therefore, there should be no rejected coins out of a well selected sample of size 280.
Chapter Review
The central limit theorem can be used to illustrate the law of large numbers. The law of large numbers states that the larger the sample size you take from a population, the closer the sample mean \(\bar{x}\) gets to \(\mu\).
Use the following information to answer the next ten exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.
Exercise 7.4.7
- What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deivation?
- What is the distribution for the mean weight of 100 25-pound lifting weights?
- Find the probability that the mean actual weight for the 100 weights is less than 24.9.
Answer
- \(U(24, 26), 25, 0.5774\)
- \(N(25, 0.0577)\)
- 0.0416
Exercise 7.4.8
Draw the graph from Exercise
Exercise 7.4.9
Find the probability that the mean actual weight for the 100 weights is greater than 25.2.
Answer
0.0003
Exercise 7.4.10
Draw the graph from Exercise
Exercise 7.4.11
Find the 90 th percentile for the mean weight for the 100 weights.
Answer
25.07
Exercise 7.4.12
Draw the graph from Exercise
Exercise 7.4.13
- What is the distribution for the sum of the weights of 100 25-pound lifting weights?
- Find \(P(\sum x < 2,450)\).
Answer
- \(N(2,500, 5.7735)\)
- 0
Exercise 7.4.14
Draw the graph from Exercise
Exercise 7.4.15
Find the 90 th percentile for the total weight of the 100 weights.
Answer
2,507.40
Exercise 7.4.16
Draw the graph from Exercise
Use the following information to answer the next five exercises: The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.
Exercise 7.4.17
- What is the standard deviation?
- What is the parameter \(m\)?
Answer
- 10
- \(\dfrac{1}{10}\)
Exercise 7.4.18
What is the distribution for the length of time one battery lasts?
Exercise 7.4.19
What is the distribution for the mean length of time 64 batteries last?
Answer
\(N\left(10, \dfrac{10}{8}\right)\)
Exercise 7.4.20
What is the distribution for the total length of time 64 batteries last?
Exercise 7.4.21
Find the probability that the sample mean is between seven and 11.
Answer
0.7799
Exercise 7.4.22
Find the 80 th percentile for the total length of time 64 batteries last.
Exercise 7.4.23
Find the \(IQR\) for the mean amount of time 64 batteries last.
Answer
1.69
Exercise 7.4.24
Find the middle 80% for the total amount of time 64 batteries last.
Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken.
Exercise 7.4.25
Find \(P(\sum x > 420)\)
Answer
0.0072
Exercise 7.4.26
Find the 90 th percentile for the sums.
Exercise 7.4.27
Find the 15 th percentile for the sums.
Answer
391.54
Exercise 7.4.28
Find the first quartile for the sums.
Exercise 7.4.29
Find the third quartile for the sums.
Answer
405.51
Exercise 7.4.30
Find the 80 th percentile for the sums.


1.3: What is the Connection between Artworks and Emotions?
There are many connections between artworks and emotions, and this chapter aims at describing the ones that are philosophically significant. For this reason, it will focus on the Expression Theory of Art and its main alternatives.
We can describe artworks as sad or cheerful for instance, and more generally as expressing emotions such as enthusiasm, admiration, and desperation. To take famous examples, Edvard Munch’s painting The Scream expresses anxiety; Ravel’s Pavane for a Dead Infanta the sadness of mourning; George Miller’s movie Mad Max the rage in front of the loss of kinship. But how are we supposed to understand and explain this connection between artworks and emotions in terms of expression? And is expression the only relation between artworks and emotions? In this chapter, we will explore three main alternatives: the first section develops the idea that artworks express the artist’s emotions; the second that art elicits and represents emotions independently of the artist’s emotions; and the third that art can be said to express emotions by themselves.
Let’s present these alternatives more closely. The first one is generally termed the Expression Theory of Art: if artworks can be described with the vocabulary of emotions, as expressing emotions, it is because they express the artist’s emotions. An additional feature is that this expression of the artist enables the audience to experience these emotions. But it seems necessary to assess such a theory: is it legitimate to explain the sadness of a poem by saying that it actually expresses the sadness of its creator? The second theory involves no reference to the artist’s emotions. A more central relation lies between the artwork and the audience, as the former is made to elicit emotions in the latter or represent emotions for the latter. However, what is the difference between elicitation and representation? And what is the connection between representing and expressing emotions? The third alternative defends precisely the idea that artworks can be said to express emotions themselves, without being necessarily connected to the artist’s emotions or those of the audience.
A historical remark must first be made in order to bring out the specificity of this issue. That artworks express the artist’s emotions is an idea that appears with romanticism, at the beginning of the 19 th century. [1] Before this period, another conception of artworks is predominant: they were considered as representations of reality. [2] This concept of representation can be understood in many ways and raises issues, but the most important for this chapter is that this concept of representation was more or less supplanted by the concept of expression, as can be seen for instance in the famous claim of the English romantic poet William Wordsworth (1770–1850) in his preface to Lyrical Ballads : “all good poetry is the spontaneous overflow of powerful feelings” (Wordsworth and Coleridge [1800] 1991, 237). Even if, according to Wordsworth, “our continued influxes of feeling are modified and directed by our thoughts” (237) and his aim was to describe and colour ordinary life, the expression of emotions became central, a criterion not only for judging but also defining poetry, and later any kind of art.
The Expression Theory of Art
In this section, we will begin with a description of the Expression Theory of Art, following the path of two famous defenders of it: Leo Tolstoy (1828–1910) in What is Art? and R.G. Collingwood (1889–1943) in The Principles of Art. Then we’ll consider several criticisms that can be addressed to this theory.
Suppose you find and describe such or such poem as expressing anger; it is rather natural to try to explain it by saying that the poem expresses the artist’s anger. More precisely, the mention of the artist’s anger functions here both as a justification of our description, and as an explanation of the poem itself, in the sense that the poet is supposed to have experienced such a feeling and produced the poem according to his feeling. However, it is possible to refine this ordinary explanation using literary and philosophical resources.
Tolstoy presents the Expression Theory of Art in the 5 th chapter of What Is Art? Its first four chapters are devoted to beauty, insofar as beauty is very often considered as a criterion to distinguish between art and non-art. Tolstoy criticises such a use of the idea of beauty in order to propose another measure: the expression of emotions. The idea of beauty is particularly contentious, and as such it can’t provide a definition of art. This is why Tolstoy considers another option, shifting art into a more general framework: “the conditions of human life” (Tolstoy 1904, 47). Art is supposed to be one of these conditions of human life, or more precisely, “one of the means of intercourse between man and man” (47). Tolstoy then defines art in this way:
To evoke in oneself a feeling one has once experienced, and having evoked it in oneself, then, by means of movements, lines, colours, sounds, or forms expressed in words, so to transmit that feeling that others may experience the same feeling—this is the activity of art.
Art is a human activity, consisting in this, that one man consciously, by means of certain external signs, hands on to others feelings he has lived through, and that other people are infected by these feelings, and also experience them. (Tolstoy 1904, 50)
This definition implies, firstly, the presence of an artist, an audience, and an emotion; secondly, that the transfer of emotion from the artist to the audience is intentional (“consciously”); thirdly, that this requires an inward evocation and a clarification of what is experienced; fourthly, that the expression is based on specific artistic media (movements, lines, colours, sounds, words).
Thus Tolstoy puts together the elements of a dynamic model of art, emphasizing agents, action, and the means entailed in the experience and practice of art. Such a model is for Tolstoy more appropriate than the criterion of beauty insofar as it grasps the nature of art via its practice.
Collingwood similarly highlights these aspects of art, using the concept of expression to define art in his own version of the Expression Theory. However, his relevance and added value in comparison with Tolstoy lies in the distinction he draws between bringing out emotions and artistic expression:
When a man is said to express emotion, what is being said about him comes to this. At first, he is conscious of having an emotion, but not conscious of what this emotion is.  While in this state, all he can say about his emotion is: “I feel … I don’t know what I feel.” From this helpless and oppressed condition he extricates himself by doing something which we call expressing himself. This is an activity which has something to do with the thing we call language: he expresses himself by speaking. It has also something to do with consciousness: the emotion expressed is an emotion of whose nature the person who feels it is no longer unconscious. It also has something to do with the way in which he feels the emotion. As unexpressed, he feels it in what we called a helpless and oppressed way; as expressed, he feels in a way from which this sense of oppression has vanished. His mind is somehow lightened and eased. (Collingwood 1960, 109–10)
At the beginning of the process of creation, there isn’t an identified “ready-made” emotion waiting for its expression, but what Collingwood calls a perturbation, an excitement; that is to say, an internal feeling, the nature and the cause of which are still undetermined. An activity, the expression of oneself (the paradigm of which is language) clarifies, makes the perturbation conscious, and transforms it into an emotion, while alleviating the individual’s perturbation. Thus, Collingwood considers the expression of the emotions in a deeper and a more subtle way, describing more precisely its actions and effects in individuals, but leaving aside other dimensions taken into account by Tolstoy, such as the necessity of an audience and the means of artistic expression. This provides the starting point of the next section.
The audience, the identity, and the existence of emotions in artistic creation
The expression theory of art by both Tolstoy and Collingwood are questionable, and we’ll raise objections corresponding to their main elements.
The first objection deals with the necessity of an audience to which to communicate the emotions. An interesting feature of Collingwood’s (1960) version of this theory is that “the expression of an emotion by speech may be addressed to someone; but if so it is not done with the intention of arousing a like emotion in him” (110, italics mine). This introduces a difference with Tolstoy’s version. According to the latter, art consists, as an activity, in passing on emotions to other people; whereas, according to the former, the relation of art to an audience is only a possibility, not a necessity. The consequence is that there are actually two versions of Expression Theory of art, named by Noël Carroll in Philosophy of Art respectively the “transmission theory” and the “solo theory” (Carroll 1999, 65).
What is the issue? The objection to the transmission theory is that “one can make a work of art for oneself” without trying to publish it (e.g., literature) or to exhibit it (e.g., painting, sculpture) (Carroll 1999, 67). Someone else who would read or see it would deem it as an artwork, but if the artist hides it, the work is still an artwork. The rejoinder is that the mere fact of writing a poem, or producing a painting, or creating a piece of music, is a use of public media that makes the emotions public, which “indicate[s] an intention to communicate to others” (67).
A solution can be developed from two similar remarks. Firstly, there is a distinction between an actual and a potential audience. An artist may not want to address such or such audience, but create an artwork designed to communicate to a potential audience. Secondly, one can question the intention to communicate to others, without questioning the communication itself. Even if it is not the intention of an artist to communicate emotions to others, an artwork can nevertheless communicate emotions. These two remarks converge in the idea that communication is a potentiality, not necessarily an intention nor even a fact. This potentiality is actualised if the artwork is presented to a public. This idea preserves both the idea that one can make a work of art for oneself, and that the medium used is publicly accessible.
There is a second objection one can make against the transmission version. It deals with the identity of the emotion supposed to be communicated from the artist to the audience. “Identity” means firstly that the audience experiences the same emotion as the artist, which implies that the artist experienced this emotion and transmits it. But is this necessarily the case? A poet can express a feeling of sorrow, but the audience feels admiration for this expression. Let’s take for instance Victor Hugo’s poem “Tomorrow, At Dawn” (1856), related to the death of his daughter:
At dawn tomorrow, when the plains grow bright,
I’ll go. You wait for me: I know you do.
I’ll cross the woods, I’ll cross the mountain-height.
No longer can I keep away from you.
I’ll walk along with eyes fixed on my mind—
The world around I’ll neither hear nor see—
Alone, unknown, hands crossed, and back inclined;
And day and night will be alike to me.
 (Hugo 2004, 199)
The emotion expressed and the emotion experienced may not be the same: Hugo expresses sadness, annihilation, and isolation, whereas the audience may well feel sadness, but also compassion, and perhaps more generally admiration, in response to such an expression of love.
“Identity” also refers to the identification of the emotions. Is the audience supposed to experience “these” emotions, as if it were possible to clearly identify our emotions? One can highlight the generality and vagueness of certain emotions. They are not necessarily individualised, but general, shared, and they are not necessarily clearly defined, but vague. In the example above, emotions overlap, and some of them are explicitly mentioned, others only suggested. It is true that this could be precisely the function of artworks to individualise and define our emotions. But such an idea fits only with a part of artistic practice: e.g., poetry is only sometimes an evocation of entangled emotions.
Ultimately, the Expression Theory of Art assumes the artist’s experience of emotions. However it is not at all certain that she must experience this emotion herself. Does a writer of a thriller experience fear, so that the thriller expresses and produces fear in the audience? It is likely they experience excitement in trying to produce fear. This objection does not deal anymore with the identity of the emotion, but with its very existence, at the roots of the potential relation between the artist and the audience. Why should an artist even experience any emotion? Of course, it would be difficult to defend the idea of artists experiencing no emotion at all. But it does not mean that emotions are the cause, the reason, or the object of creation. In this sense, emotions are not always necessary to creation.
Eliciting and Representing Emotions
These criticisms do not imply the rejection of expression of/and emotions in art, but only of the idea that art must be defined as an expression of the artist’s emotions to an audience by certain means. Moreover, such a criticism allows other possible descriptions of the relation between artworks and emotions, such as elicitation and representation, which we consider in this section.
It is a classical idea of the rhetorical approach to literary works that they elicit emotions. Rhetoric describes the techniques by which one is able to produce reactions in an audience according to context. In the judicial field, the lawyer has to convince judges regarding past facts in order to win the case. In the political field, politicians and ordinary citizens have to convince each other to make a decision about the future, according to what is useful or detrimental to the country. In the field of public eulogies, the speaker has to praise or comfort. In all these cases, the rhetoric provides non-linguistic means such as advice about posture, gestures, etc., and linguistic means such as patterns of arguments (for instance, enthymemes) and figures of speech, that both play on and elicit emotional reactions, in order to convince and persuade.
Beyond these specific fields, literary criticism and more generally aesthetics use (among other things) the figures of speech studied and systematised by rhetoric. They do so in order not only to describe literary artworks and the style of artworks, but also to show the way artists and literary writers use these figures of speech as means to elicit emotions. Let’s consider the first stanza of Rimbaud’s “Orphans’ New Year Gifts” (1870):
The room is full of shadow and the sad
Faint whispering of two little ones,
Heads still heavy with dreams
Beneath the long white curtain, stirring slightly …
Outside, birds cluster for warmth,
Wings drooping against the grey sky.
And the New Year, dragging mist,
Trailing its snow-dress on the ground,
Smiles through tears, and shivers a song … (Rimbaud 2001, 3)
A significant feature is its general structure, organised around the contrast of two locations, a room and the outside, but also the continuity established between them by the echo of the shadow of the room in the sad whispering of the orphans, on one hand, and the mist of the New year and its “smile through tears,” on the other. But more important is the personification of the New Year, which drags mist, trails a snow-dress, smiles through tears, and shivers a song, as a presence outside that echoes the orphans’ sadness within. This figure of speech contributes to the eliciting of visual and emotional impressions, as a picture materialises gradually and a feeling of sadness arises, one that then envelops the whole stanza.
An alternative way to describe this elicitation of emotions can be found in T.S. Eliot’s essay on “Hamlet and His Problems,” under the label of “objective correlative.” There he tries to explain what is, according to him, Hamlet ’s failure. A starting point is his agreement with the idea that “the essential emotion of the play is the feeling of a son [Hamlet] towards a guilty mother” (Eliot 1939, 144).  By contrast, here is the rule T.S. Eliot defends:
The only way of expressing emotion in the form of art is by finding an “objective correlative”; in other words, a set of objects, a situation, a chain of events which shall be the formula of that particular emotion; such that when the external facts, which must terminate in sensory experience, are given, the emotion is immediately evoked. (Eliot 1939, 145)
The emotion of the play and, more generally, of a literary work is to be found in an objective correlative, which is an “exact equivalent” characterised by a “complete adequacy of the external to the emotion.” That’s to say, more concretely, the emotion is found in a description of situations, events, characters, reactions, that shows this emotion, and therefore in a full representation of the emotion that elicits it in the audience. According to T.S. Eliot one finds a good example of objective correlative in Macbeth :
You will find that the state of mind of Lady Macbeth walking in her sleep has been communicated to you by a skilful accumulation of imagined sensory impressions; the words of Macbeth on hearing of his wife’s death strike us as if, given the sequence of events, these words were automatically released by the last events in the series. (Eliot 1939, 145)
Nevertheless, it would be superficial to present the elicitation of emotions as a causal production of emotion by means of figures of speech. As Danto puts it in his discussion of Aristotle and rhetoric in the last part of The Transfiguration of the Common place ,
if it be anger they [rhetoricians] intend to arouse, they will know how to characterize the intended object of the anger in such a way that anger toward that object is the only justifiable response. . . . After all, like beliefs and actions–in contrast with bare perceptions and mere bodily movements–emotions–in contrast perhaps with bare feelings–are embedded in structures of justification. There are things we know we ought to feel given a certain characterization of the conditions we are under. (Danto 1981, 169)
To elicit emotions for a (literary) artwork is not merely a matter of causal relation: the artwork, its figures of speech, or its style, if successful, are such that one should have a determinate emotional response. In other words, not any emotion is admissible but only some of them are justifiable in front of a particular artwork.
To conclude this section, it is possible to argue that, even though artworks do not necessarily express the artist’s emotions, they elicit emotions in the audience by artistic means such as figures of speech in literary artworks, or representation of emotions in the choice of a certain “correlated” objectivity, such as a series of actions in a play or a set of forms and colours in a painting.
An Autonomous Expression
The idea defended in the last section, according to which artworks can represent emotions, allows us to come back to the notion of expression, but in a different way to the Expression Theory of Art elaborated in the first section. T.S. Eliot uses “representation” and “expression” almost indistinguishably, but these terms should be refined. What does it mean for artworks not only to represent but also to express emotions by themselves? A closer analysis of the notion of expression is needed here.
In our ordinary judgments, we talk about the sadness of a poem, the fact that a certain piece of music is described as joyful and another one as desperate, or that a particular style for a building is cold. Hence, the question: Can artworks be said to express emotions themselves? And why would it be a problem? As Oets K. Bouwsma explains in “The Expression Theory of Art,”
The use of emotional terms—sad, gay, joyous, calm, restless, hopeful, playful, etc.—in describing music, poems, pictures, etc., is indeed common. So long as such descriptions are accepted and understood in innocence, there will be, of course, no puzzle. But nearly everyone can understand the motives of [the] question “How can music be sad?” and of his impulsive “It can’t, of course.” (Bouswma 1959, 74)
How can we explain such a paradoxical use of emotional terms, which seems to be at the same time accepted and impossible? What is assumed in “Music can’t be sad” is “… as someone can be sad.” It is the reason why, according to Bouswma, it is interesting to consider and compare several uses of “sad,” such as: “Cassie is sad,” “Cassie’s dog is sad,” “Cassie’s book is sad,” and “Cassie’s face is sad.” In the first case, one can imagine Cassie learning the death of a next of kin and crying, or reading a wonderful but sad poem, and becoming sad herself, crying or not. In the second case, it makes sense to say that the dog can be sad, but could it cry? One does not expect the dog to express sadness in all the ways human beings do (a dog does not restrain its howls). One can paraphrase the third case saying that this book makes Cassie sad. And in the last case, one can easily describe obvious signs of sadness, however there is no guarantee that she is really sad.
What conclusion can we draw now as regards to the assertion “the music is sad”? This assertion is similar neither to Cassie being sad and crying because of a death in her family, nor to Cassie being sad but not crying, nor to her dog being sad but not crying: a song is neither crying nor holding back tears! It is much more similar to “the book is sad,” understood as producing sadness, but particularly as being sad in itself, as a face can be sad, be it a real face or a drawing: the book, the music, and the face express sadness themselves but in a specific way.
How can one account for this expression? Are these examples really on the same level? One can find an answer in Nelson Goodman’s theory of expression in Languages of Art , which is based on the concepts of exemplification and metaphor.
An expression can be considered as a kind of exemplification. Exemplification refers to a certain relation of something to some properties. For instance, a sample of fabric exemplifies cashmere, in that (1) it is made of cashmere and therefore possesses this property to be made of cashmere, (2) qua sample, it refers to this property. Indeed, something can refer to cashmere without possessing this property of being made of cashmere, as it is the case in a description of this fabric.
However, such a definition of exemplification is not enough to account for the description of an artwork as expressing such or such emotion. It is true that a sad poem possesses this property of being sad, and refers to sadness in general, but how could a sad poem be “made of sadness” or be described literally as sad? The poem is not described literally as sad but metaphorically; the possession of the property is not literal but metaphorical. [3] Therefore, a poem exemplifies sadness in that (1) it refers to sadness and (2) possesses sadness (3) metaphorically.
One could object that this idea of metaphorical possession is obscure, as if only literal possession were without difficulty (for instance, in “this stone is hard”). However, among the different ways of describing things, events, people, etc., it is possible to attribute properties in a metaphorical way (and then to see in this possession an exemplification of the property in question). One could reply that, because it is a metaphor, the sadness is not “really” in the poem. However, the fact is that such a metaphorical description is sometimes far more objectively true than a literal one. To describe someone as a “Don Quixote” or a “Don Giovanni” (which means that this person possesses metaphorically and exemplifies the properties of Don Quixote or Don Giovanni) does not necessarily raise a question, whereas to describe literally such or such entity as a virus or an organism raises sometimes real difficulties and disagreements between scientists. In this sense, that a song or a poem expresses such or such emotion can be perfectly objective.
Conclusion
To conclude, there is certainly something right in the ordinary claim that artworks express emotions. This means that the issue lies somewhere else, in the philosophical accounts of such a claim. While a number of accounts can be found in contemporary philosophy, not all of them are likely to make sense of the ordinary claim about artwork’s expression of emotions.
More precisely, all the elements mentioned by Tolstoy are interesting for those who are passionate about arts: the relation of an artist and audience, the sharing of emotions, and the means used to do this. They all belong to our experience and practice of art, and one virtue of Tolstoy’s analysis is precisely to consider artworks in this broader context: our practices and experiences. At the same time, it raises a philosophical issue about what is essential in this general description if one wants to understand artworks’ specific feature regarding emotions: expressivity.
This chapter aims at showing the intrinsic expressivity of artworks, in addition to their capacity to elicit and represent emotions, ultimately leaving aside the artist’s and audience’s experience of emotions. The idea is neither to deny the reality of such an experience, nor its importance for the artist and the audience, but to highlight how artworks’ expressivity can be found in themselves, because they are themselves describable as expressing such or such emotion. To go further in this direction, one could say that the key to expressivity can be found in the functioning of works of art, for instance, the way a painting describes a landscape, possesses such or such characteristics (colours or lines), and refers to sadness or joy. What it is (characteristics) and what it does (description and reference) are central to understand how an artwork finally expresses emotions. The next step would be to come back to our experience and practice: How do they shape our ability to grasp the emotions expressed in artworks? What is the role of experience and practice in the understanding of the artwork’s expressivity?
references
Bouswma, Oets K. 1959. “The Expression Theory of Art.” In Aesthetics and Language , edited by William Elton, 73–99. Oxford: Blackwell.
Carroll, Noël. 1999. Philosophy of Art . London and New York: Routledge.
Collingwood, Robin G. 1960. The Principles of Art . Oxford: Clarendon Press.
Danto, Arthur. 1981. The Transfiguration of the Commplace . Cambridge, MA: Harvard University Press.
Eliot, Thomas Stearns. 1939. Selected Essays . London: Faber and Faber Limited.
Hugo, Victor. 2004. Selected Poems of Victor Hugo . Translated by E. H. and A. M. Blackmore. Chicago: Chicago University Press.
Goodman, Nelson. 1968. Languages of Art . Indianapolis: The Bobs-Merrill Company.
Rimbaud, Arthur. 2001. Collected Poems . Edited by Martin Sorrell. Oxford: Oxford University Press.
Tolstoy, Leo. 1904. What is Art? Translated by Aylmer Maude. New York: Funk & Wagnalls.
Wordsworth, William and Coleridge, Samuel Taylor. [1800] 1991. Lyrical Ballads . Edited by R. L. Brett and A. R. Jones. 2nd ed. London: Routledge.
- Particularly in Great Britain with William Wordsworth’s poetry, for instance his Lyrical Ballads (1798), or in Germany with Caspar David Friedrich’s paintings, for instance “Wanderer above the Sea of Fog” (1818). ↵
- The main representative works of this tradition are Plato’s Republic and Aristotle’s Poetics , even if the overlapping of their concept of imitation and the concept of representation is problematic. The question is indeed: Do artworks have to imitate reality? If so, what does "imitate" mean here? And what is the reality that would have to be imitated? ↵
- Goodman (1968) draws a distinction between literal and metaphorical descriptions as follows. A description is literal when the words are used in their ordinary, routine way (e.g., to use “green” to describe the grass). But it becomes metaphorical when the words are applied to new things that first of all resist such a description and then accept it (e.g., to use a word of colour in order to describe a mood). ↵


16.2: Vector Addition
The most common thing we will need to do with many vector quantities is to add them up. The sum of these vector quantities is the net vector quantity. For example, if we have a number of forces acting on a body, the sum of those forces is known as the net force.
The sum of any number of vectors can be determined geometrically using the following strategy. Starting with one of the vectors as the base, we redraw the second vector so that the tail of the second vector begins at the tip of the first vector. We can repeat this with a third vector, a forth vector and so on, putting the tail of each vector at the tip of the last vector until we have added taken all vectors into account. Once the vectors are all drawn tip to tail, the sum of all the vectors will be the vector connecting the tail of the first vector to the tip of the last vector.
In practice, the easiest way to determine the magnitude and direction of the sum of the vectors is to add the vectors in component form . This starts by separating each vector into \(x\), \(y\), and possibly \(z\) components. As we can see in the diagram below, the \(x\) component of the sum of all the vectors will be the sum of all the \(x\) components of the individual vectors. Similarly, the \(y\) and \(z\) components of the sum of the vectors will be the sum of all the \(y\) components and the sum of all the \(z\) components respectively.
Once we find the sum of the components in each direction, we can either leave the net vector in component form, or we can use the Pythagorean theorem and inverse tangent functions to convert the vector back into a magnitude and direction as detailed on the previous page on vectors .
Figure \(PageIndex{1}\): Vide lecture covering this section, delivered by Dr. Jacob Moore. YouTube source: https://youtu.be/0tv92MX2_ro .
Example \(\PageIndex{1}\)
Determine the sum of the force vectors in the diagram below. Leave the sum in component form.
- Solution:
Example \(\PageIndex{2}\)
Determine the sum of the force vectors in the diagram below. Give the sum in terms of a magnitude and a direction.
- Solution:
Example \(\PageIndex{3}\)
Determine the sum of the force vectors in the diagram below. Leave the sum in component form.
- Solution:


8: Confidence Intervals
In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
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- 8.1: Prelude to Confidence Intervals
- In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
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- 8.3: A Single Population Mean using the Student t-Distribution
- We rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation ss as an estimate for σσ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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- 8.5: Confidence Interval - Home Costs (Worksheet)
- A statistics Worksheet: The student will calculate the 90% confidence interval for the mean cost of a home in the area in which this school is located. The student will interpret confidence intervals. The student will determine the effects of changing conditions on the confidence interval.
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- 8.6: Confidence Interval -Place of Birth (Worksheet)
- A statistics Worksheet: The student will calculate the 90% confidence interval the proportion of students in this school who were born in this state. The student will interpret confidence intervals. The student will determine the effects of changing conditions on the confidence interval.
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- 8.7: Confidence Interval -Women's Heights (Worksheet)
- A statistics Worksheet: The student will calculate a 90% confidence interval using the given data. The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


5.1: Polyhedra
Lesson
Let's investigate polyhedra.
Exercise \(\PageIndex{1}\): What are Polyhedra?
Here are pictures that represent polyhedra :
Here are pictures that do not represent polyhedra:
- Your teacher will give you some figures or objects. Sort them into polyhedra and non-polyhedra.
- What features helped you distinguish the polyhedra from the other figures?
Exercise \(\PageIndex{2}\): Prisms and Pyramids
- Here are some polyhedra called prisms .
Here are some polyhedra called pyramids .
- Look at the prisms. What are their characteristics or features?
- Look at the pyramids. What are their characteristics or features?
- Which of these nets can be folded into Pyramid P? Select all that apply.
-
Your teacher will give your group a set of polygons and assign a polyhedron.
- Decide which polygons are needed to compose your assigned polyhedron. List the polygons and how many of each are needed.
- Arrange the cut-outs into a net that, if taped and folded, can be assembled into the polyhedron. Sketch the net. If possible, find more than one way to arrange the polygons (show a different net for the same polyhedron).
Are you ready for more?
What is the smallest number of faces a polyhedron can possibly have? Explain how you know.
Exercise \(\PageIndex{3}\): Assembling Polyhedra
- Your teacher will give you the net of a polyhedron. Cut out the net, and fold it along the edges to assemble a polyhedron. Tape or glue the flaps so that there are no unjoined edges.
- How many vertices , edges , and faces are in your polyhedron?
Summary
A polyhedron is a three-dimensional figure composed of faces.  The ends of the edges meet at points that are called vertices.
A polyhedron always encloses a three-dimensional region.
The plural of polyhedron is polyhedra. Here are some drawings of polyhedra:
A prism is a type of polyhedron with two identical faces that are parallel to each other and that are called bases . The bases are connected by a set of rectangles (or sometimes parallelograms).
A prism is named for the shape of its bases. For example, if the base is a pentagon, then it is called a “pentagonal prism.”
A pyramid is a type of polyhedron that has one special face called the base. All of the other faces are triangles that all meet at a single vertex.
A pyramid is named for the shape of its base. For example, if the base is a pentagon, then it is called a “pentagonal pyramid.”
A net is a two-dimensional representation of a polyhedron. It is composed of polygons that form the faces of a polyhedron.
A cube has 6 square faces, so its net is composed of six squares, as shown here.
A net can be cut out and folded to make a model of the polyhedron.
In a cube, every face shares its edges with 4 other squares. In a net of a cube, not all edges of the squares are joined with another edge. When the net is folded, however, each of these open edges will join another edge.
It takes practice to visualize the final polyhedron by just looking at a net.
Glossary Entries
Definition: Base (of a Prism or Pyramid)
The word base can also refer to a face of a polyhedron.
A prism has two identical bases that are parallel. A pyramid has one base.
A prism or pyramid is named for the shape of its base.
Definition: Face
Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.
Definition: Net
A net is a two-dimensional figure that can be folded to make a polyhedron.
Here is a net for a cube.
Definition: Polyhedron
A polyhedron is a closed, three-dimensional shape with flat sides. When we have more than one polyhedron, we call them polyhedra.
Here are some drawings of polyhedra.
Definition: Prism
A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.
Here are some drawings of prisms.
Definition: Pyramid
A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.
Here are some drawings of pyramids.
Definition: Surface Area
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
For example, if the faces of a cube each have an area of 9 cm 2 , then the surface area of the cube is \(6\cdot 9\), or 54 cm 2 .
Practice
Exercise \(\PageIndex{4}\)
Select all the polyhedra.
- A
- B
- C
- D
- E
Exercise \(\PageIndex{5}\)
- Is this polyhedron a prism, a pyramid, or neither? Explain how you know.
- How many faces, edges, and vertices does it have?
Exercise \(\PageIndex{6}\)
Tyler said this net cannot be a net for a square prism because not all the faces are squares.
Do you agree with Tyler? Explain your reasoning.
Exercise \(\PageIndex{7}\)
Explain why each of these triangles has an area of 9 square units.
(From Unit 1.3.2)
Exercise \(\PageIndex{8}\)
- A parallelogram has a base of 12 meters and a height of 1.5 meters. What is its area?
- A triangle has a base of 16 inches and a height of \(\frac{1}{8}\) inches. What is its area?
- A parallelogram has an area of 28 square feet and a height of 4 feet. What is its base?
- A triangle has an area of 32 square millimeters and a base of 8 millimeters. What is its height?
(From Unit 1.3.3)
Exercise \(\PageIndex{9}\)
Find the area of the shaded region. Show or explain your reasoning.
(From Unit 1.1.3)


In high school, students are required to attend school—it’s the law. However, college is a choice. Students can choose which college to attend, what to major in while in college, what professors to take, and what career path they want to follow after college. A key point for you, as a student, to understand is that for whatever the reason, you have made a choice to be in college. Ultimately, you have a choice to manage that decision responsibly, which in part requires that right attitude toward college if you are to be successful in the end.
Students typically begin college with an optimistic view of their ability to succeed beyond some of the normal apprehension regarding what college will be like. After a few weeks or months, students might begin to have some doubts about their ability to succeed, and that is completely natural. However, it is the attitude that students adopt at this point that can “make” or “break” their academic career.
Victims and Creators
According to Skip Downing (2008), students’ general attitude toward a given situation tends to fall into one of two general categories: a Victim or a Creator (see Table 4-1).
Table 4-1. Behavioral Indicators of Victims and Creators
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Victims
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Creators
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Focus on their weaknesses related to a situation
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Look to use their strengths to over- come obstacles
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Complain and make excuses
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Acknowledge the problem and seek solutions
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Blame someone else
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Take personal responsibility
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See problems as permanent, catastrophic events
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See problems as temporary events that they can overcome
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Repeat behaviors that have not been successful in the past
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Actively seek new information and take new actions based on this information
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Predict defeat in the face of obstacles
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Look for better ways to approach a problem
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Use negative self-talk like “This professor is stupid.”
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Use more positive self-talk like “I am having troubles focusing in this class so I am going to prepare for class and sit in the front.”
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Victims tend to believe that they have little control over the world and what happened to them in a given situation. Often, victims continue to repeat behaviors that have not proven to be effective in the past, in part because it is the easier thing to do. Typically, they understand what they should have done in a situation but tend to respond, “Yes … but…,” followed by an explanation of who is to blame or an excuse. On the other hand, creators accept personal responsibility for themselves and their thoughts, beliefs, and actions. When their thinking and behavior has been proven to be ineffective, they seek out help and new information and try something new (see Figure 4-1).
Overall, in a study of nearly 1,000 new undergraduate students, researchers found that those students who adopted an attitude of a creator were more successful in meeting their goals in continuing in college compared to students who adopted an attitude of a victim (Vallerand & Bissonnette, 1992).
Figure 4-1. Differing Responses of Victims and Creators
Source: Downing,Skip. (2008)
It is important to note that students are not born with the mindset of victim or creator in their approach to life. Students can choose to adopt the mindset that they want to adopt. For instance, students can choose to spend their precious time and energy blaming others and complaining about all of the obstacles (behaving as a victim) which does nothing to change the outcome, or they can choose to seek out new information and assistance from others that will help improve the outcome (behaving as a creator).
If you find that you (or a fellow student) is behaving more like a victim in a given circumstance, think about how you are reacting and choose to adopt a creator mindset and action plan.