Rolling a fair eight-sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard deviation of 2.291. Assume that n eight-sided dice are rolled many ties and the mean of the n outcomes is computed each time.
A. Find the mean and standard deviation of the resulting distribution of sample means for n=81
B. Find the mean and standard deviation of the resulting distribution of sample means for n= 121.
C. Why is the standard deviation in Part A different from the standard deviation in Part B?