Refer to Exercise 4.108. To evaluate how accurately the sample mean y estimates the population mean m, we need to know the chance of obtaining a value of y that is far from μ. Suppose it is important that the sample mean y is within five units of the population mean m. Find the following probabilities for each of the three sample sizes, and comment on the accuracy of using y to estimate μ.
a. P(y-bar ≥ 105)
b. P(y-bar ≤ 95)
c. P(95 ≤ y-bar ≤ 105)