A population has a mean of 400 and a standard deviation of 80. Suppose a sample of size 125 is selected and (x-bar) is used to estimate (mu).
a. What is the probability that the sample mean will be within +/- 8 of the population mean (to 4 decimals)?
b. What is the probability that the sample mean will be within +/- 13 of the population mean (to 4 decimals)?