Bright Star Financial Advisers receives a mean of 19.5 applications per week for a personal financial review. Each review requires one day of an analyst's time to prepare a review. Assume that requests received during any week are assigned to an analyst for completion during the following week. If the analysis is not completed during the second week the customer will cancel.
a. How many analysts should be hired so that the company can claim that 90% of the reviews will be completed during the second week?
b. What is the probability that two of the analysts hired for part a would have no clients for an entire week?
c. Suppose that they decided to hire one less analyst than determined in part (a). What is the probability that customers would cancel given this staffing level?
d. Given the number of analysts hired in part c, what is the probability that two analysts would be idle for an entire week?