The binomial distribution is always finite. You can only have a finite number of values. While the normal distribution is defined over the entire real number line. So the probability, if you have a mean of minus 5 and a standard deviation of 10, the probability of getting 1,000 here is very, very low. But there is some probability that all of the atoms in my body just arrange perfectly that I fall through the seat I'm sitting on. It's very unlikely. And it probably won't happen in the life of the universe.