Answer each question to the best of your ability. Show your calculations (they can be verified on a calculator). Your final answer should be in the form of a complete sentence.

Rolling a fair 12-sided die produces a uniformly distributed set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Assume that n such dice are rolled many times and the mean of the n outcomes is computed each time.

1. Find the mean and standard deviation of the resulting distribution of sample means for n = 100.

(3 points)

2. Find the mean and standard deviation of the resulting distribution of sample means for n = 81.

(3 points)

3. Why is the standard deviation in part (a) different from the standard deviation in part (b)? (4 points)