4. One clerk is on duty at the information desk of a BPH clinic. The clerk can process information requests in an average time of 3 minutes, and this can be described by a negative exponential distribution that has a mean of 3. Requests are received at a rate of 15 per hour (Poisson distribution). Find:

a. The expected number of requests waiting to be addressed.

b. The average time people spend waiting in line for service.

c. In an 8-hour shift, how many hours is the clerk idle?

d. What is the probability that there are fewer than four people at the information desk (excluding the clerk)?