Runners in a race have a mean finishing time of 91 minutes and a standard deviation of 16 minutes. If

we assume the runner's times are normally distributed, answer the following:

a) What is the probability that the finishing time of a single randomly selected runner is within 5 minutes

of the population mean?

b) What is the probability that the sample mean finishing time of 9 runners is within 5 minutes of the

population mean?

c) What is the probability that the sample mean finishing time of 49 runners is within 5 minutes of the

population mean?

d) Compare the probabilities. What does this tell us about the benefits of a large sample size for

estimating the population mean?