Please help with this homework assignment! a-e

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your operations and supply chain course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that the students arrive at a rate of four per hour and the distribution is approx Poisson. Assistance time averages 10.09 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline. is FCFS.

a. calculate the percentage utilization of the graduate student.

b. calculate the average number of students in the system, excluding the graduate student service.

c. calculate the average time in the system.

d. calculate the probabilities of four or more students being in line or being served.

e. before a test, the arrival of students increases to 5.5 per hour, on average. What will the new average line length be?