As reported by Runner's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Do the following for the variable "finishing time" of finishers in the New York City 10-km run.
a. Find the sampling distribution of the sample mean for samples of size 4.
b. Repeat part (a) for samples of size 9.
c. Construct graphs similar to those shown in Fig. 7.4 on page 293.
d. Obtain the percentage of all samples of four finishers that have mean finishing times within 5 minutes of the population mean finishing time of 61 minutes. Interpret your answer in terms of sampling error.
e. Repeat part (d) for samples of size 9.