$2\mathrm{.}8$ Ocala Software Systems operates its support center with one consultant. Customers are queued to receive their services when the consultant is busy. The customer calls follow a Poisson probability distribution with an arrival rate of five calls per hour. On average, it takes $7\mathrm{.}5$ minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution.

a$.$ What is the service rate in terms of customers per hour?

b$.$ What is the probability that no customers are in the system and the consultant is idle?

c$.$ What is the average number of customers waiting for a consultant?

d$.$ What is the average time span between a customer picking up the phone seeking help and hanging up after being served?