Refer to Exercise 4.108. To evaluate how accurately the sample mean estimates the popul...

Refer to Exercise 4.108. To evaluate how accurately the sample mean estimates the population mean μ , we need to know the chance of obtaining a value of that is far from μ . Suppose it is important that the sample mean is within 5 units of the population mean μ . Find the following probabilities for each of the three sample sizes and comment on the accuracy of using to estimate μ .

REFERENCE:

4.108 : Random samples of size 5, 20, and 80 are drawn from a population with mean μ = 100 and standard deviation σ = 15.

a. Give the mean of the sampling distribution of for each of the sample sizes 5, 20, and 80.

b. Give the standard deviation of the sampling distribution of for each of the sample sizes 5, 20, and 80.

c. Based on the results obtained in parts (a) and (b), what do you conclude about the accuracy of using the sample mean as an estimate of population mean μ ?