Assume a very large normally distributed population of scores on a test with mean 70 and standard deviation 7.

a. Find an interval that includes 95% of the population.

b. Suppose you randomly sample a single member from this population. Find an interval so that you are 95% confident that this member’s score will be in the interval.

c. Now suppose you sample 30 members randomly from this population. Find an interval so that you are 95% confident that the average of these members’ scores will be in the interval. 

d. Finally, suppose you sample 300 members randomly from this population. Find an interval so that you are 95% confident that the average of these members’ scores will be in the interval.

e. Explain intuitively why the answers to parts a—d are not all the same.