Problem $10-18($Algo$)$

A study$-$aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in

your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that

students arrive at a rate of five per hour and the distribution is approximately Poisson. Assistance time averages $5$ minutes, distributed

exponentially. Assume population and line length can be infinite and queue discipline is FCFS$.$

o$.$ Calculate the percentage utilization of the graduate student.

Note: Round your answer to $2$ decimal places.

b$.$ Calculate the average number of students in the system, including the students at the graduate student service desk.

Note: Round your answer to $1$ decimal place.

c$.$ Calculate the average time in the system.

Note: Round your answer to $1$ decimal place.

d$.$ Calculate the probability of four or more students being in line or being served.

Note: Round your Intermedlate calculations to $3$ decimal places and final answer to $1$ decimal place.