Dave Wilson, president of the Graduate Management Admissions Council (GMAC), reported the results of a recent GMAC survey of 5,829 MBA graduates. The average annual base salary increased to $88,626. The high annual base salary was set in 2001 at approximately $92,500 after adjusting for inflation.

a. Assuming that the standard deviation of the salary and bonus for new MBAs was $40,000, calculate the probability that a randomly selected sample of size 5,829 graduates would yield a sample mean of at most

$88,626 if the population mean equaled $92,500.

b. Is it plausible that the average annual base salaries for both 2001 and recent graduates were actually the same? Support your assertions.

c. Determine the probability that at least half of 5 MBA students who graduated in 2001 would get annual base salaries of at least $92,500.