The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour.

a. What is the probability that no requests for assistance are in the system?

b. What is the average number of requests that will be waiting for service?

c. What is the average waiting time in minutes before service begins?

d. What is the average time at the reference desk in minutes (waiting time plus service time)?

e. What is the probability that a new arrival has to wait for service?