3 Consider an emergency room. An average of 10 patients arrive per hour (interarrival times are exponential). Upon entering, the patient fills out a form. Assume that this always takes 5 minutes. Then each patient is processed by one of two registration clerks. This takes an average of 7 minutes

(exponentially distributed). Then each patient walks 2 minutes to a waiting room and waits for one of 4 doctors. The time a doctor takes to see a patient averages 20 minutes, with a standard deviation of 10 minutes.

a On the average, how long does a patient spend in the emergency room?

b On the average, how much of this time is spent waiting for a doctor?
c What percentage of the time is each doctor busy?