A new dental clinic at which only one dentist works is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that patients will arrive at the desk at a rate of 36 per hour. It takes an average of 1.25 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. (a) What is the probability that there are exactly three patients in the system? (b) What is the probability that there are fewer than four patients in the system? (c) The cost of waiting time, in terms of patient unhappiness with the dental clinic, is $16 per hour of time spent waiting in line. Find the expected waiting costs over an 8-hour day.
