In this problem, assume that all inter-arrival and service times are exponentially distributed.

a. At present, the finance department and the marketing department each has its own typists. Each typist can type 25 letters per day. Finance requires that an average of 20 letters per day be typed, and marketing requires that an average of 15 letters per day be typed. For each department, determine the average length of time that elapses between a request for a letter and completion of the letter.

b. Suppose that the two typists are grouped into a typing pool; that is, each typist is now available to type letters for either department. For this arrangement, calculate the average length of time between a request for a letter and completion of the letter.

c. Comment on the results of parts a and b.

d. Under the pooled arrangement, what is the probability that more than 0.2 day will elapse between a request for a letter and start of the letter?