Question: Ten-sided Dice and the Central Limit Theorem. Rolling a fair 10-sided die produces a uniformly distributed set of numbers between 1 and 10 with a

Ten-sided Dice and the Central Limit Theorem. Rolling a fair 10-sided die produces a uniformly distributed set of numbers between 1 and 10 with a mean of 5.5 and a standard deviation of 2.872. Assume that n 10-sided dice are rolled many times 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 = 49.

b. Find the mean and standard deviation of the resulting distribution of sample means for n = 400.

c. Why is the standard deviation in part a different from the standard deviation in part b?

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