At Pleasant Valley High, a very large school, math test scores are distributed normally with a mean of 50 points and a standard deviation of 20 points.

a) What percentage of scores fall between 30 points and 70 points? What percentage of scores falls between 10 and 90 points?

b) If we drew a random sample of 100 students’ scores, what is the expected value for the mean of the sample?

c) Considering all possible samples of 100 (sampling with replacement makes this an infinite number of samples), what is the expected value for the mean of all the sample means?

What is the standard deviation of this distribution of sample means? What term is used for this special type of standard deviation?