Question: A clerk of court is responsible for receiving and logging legal documents that are to be placed before the various judges to review and sign. She receives these documents on a first-come, first-served basis. Lawyers' couriers arrive before the clerk at an average rate of eight per hour, according to a Poisson distribution. The time it takes the clerk to process the documents is normally distributed, with an average of six minutes and a standard deviation of two minutes.
(a) What is the probability that a courier will have to wait for service?
(b) On average, how many couriers will be waiting for service?
(c) How long is the average wait for service?