An administrator in a small suburban hospital is concerned with the waiting lines in the emergency room, which is always staffed by at least one doctor. Patients arrive on average at the rate of 14 per hour. They are served on a first-come, first-served, basis. On average, one doctor, working alone, can treat a patient in 5 minutes. For each additional doctor added, 2 more patients can be seen in a hour by all doctors working together, on average. (Assume the Poisson arrivals and exponential service times) The administrator has set the objective that, on average, there should not be more than 6 patients waiting to see a doctor.

With the minimum number of doctors working together

1. What is the chance that a patient will have to wait for service?

a. What is the chance that a patient won't have to wait for service?

b. What is the chance that no patients will arrive in a five minute period?