Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was $3267; in 2003, the average annual Medicare spending per enrollee was $6883. Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditures. Assume the population standard deviation for 2003 was $2000.
a. Show the sampling distribution of the mean amount of Medicare spending for a sample of fifty 2003 enrollees.
b. What is the probability that the sample mean will be within +/- $300 of the population mean?
c. What is the probability that the sample mean will be greater than $7500? If the consulting firm tells you the sample mean for the Medicare enrollees it interviewed was $7500, would you question whether the firm followed correct simple random sampling procedures? Why or why not?