Question: A librarian at a college library, on an average, could process 22 students during one hour. On an average, a student arrives to her at every 4 minutes. Assume it is a single-server waiting line model.

(a) Determine the mean arrival rate and the mean service rate.

(b) Determine the probability that a student will have an empty queue.

(c) Determine the average number of students in the queue and the average number of students in the system.

(d) Determine the average waiting time in the queue and the average total time in the system for a student.

(e) Find the utilization factor of the librarian.