1. A new dental clinic with only one dentist is considering setting up an information desk manned by a single employee. The clinic is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.
What is the probability that the clinic is empty (except for the information desk employee & the dentist)?
What is the probability that there are one or more patients in the system?
What is the probability that there are four patients in the system?
What is the probability that there are four or more patients in the system?
2. Assume that the information desk employee in Question 1 earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the clinic, is $12 per hour of time spent waiting in line. What is the total expected costs over an 8-hour day?