Rolling a fair ten dash sided ten-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 ten dash sided ten-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 nequals =144

The mean of the resulting distribution of sample means is. ?(Round to the nearest tenth as? needed.)

The standard deviation of the distribution of sample means is ?(Round to the nearest thousandth as? needed.)

b. Find the mean and standard deviation of the resulting distribution of sample means for nequals =81

The mean of the resulting distribution of sample means is. ?(Round to the nearest tenth as? needed.)

The standard deviation of the distribution of sample means is ?(Round to the nearest thousandth as? needed.)

c. Why is the standard deviation in part a different from the standard deviation in part? b? Choose the correct answer below.

A. With larger sample sizes? (as in part? a), the means tend to be closer? together, so they have less? variation, which results in a smaller standard deviation.

B. With larger sample sizes? (as in part? a), the means tend to be further? apart, so they have more? variation, which results in a bigger standard deviation.

C. With smaller sample sizes? (as in part? b), the means tend to be closer? together, so they have less? variation, which results in a smaller standard deviation.

D. With smaller sample sizes? (as in part? b), the means tend to be further? apart, so they have more? variation, which results in a smaller standard deviation.