.Child.CARE is a walk-in pediatric clinic. Patients arrive at Child.CARE at a rate of 8 per hour according to a Poisson distribution. Currently, the clinic has three physicians who work independently. As patients arrive to Child.CARE, they wait on a single queue for the first available physician to serve them. Each physician spends, on average, 20 minutes with each patient. The service time follows a negative exponentially distribution.

a) What is the probability of all physicians being idle?

b) What is the probability that a customer will have to wait?

c) What is the impact on the clinic service and efficiency if Child.CARE adopts the policy of not more accepting patients when there are already 10 patients in the waiting room? Please explain and quantify using appropriate metrics