The economic downturn after the financial crisis early in the current century affected all salaried employees, certainly starting MBA employees. While the average starting salary varies depending on the source of the study and field of emphasis, one respected source shows an average annual starting base salary of $88,626. The high starting 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 $20,000, 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. Assuming the distribution of salaries was normal with a mean of $92,500, determine the probability that at least half of 5 MBA graduates would get annual base salaries of at least $92,500.