The computer lab at State University has a help desk to assist students working on computer

spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help.

Students are served based on a first$-$come, first$-$served priority rule. Students arrive at the help desk at

the rate of $4$ every $10$ minutes. The average service time is $2$ minutes. The Poisson distribution is

appropriate for the arrival rate and service times are exponentially distributed.

a$)$ What is the average time a student is in the lab?

b$)$ What is the average number of students in the lab?

c$)$ What is the average number of students waiting to receive service?

d$)$ What is the average time a student is in the queue?

e$)$ What is the probability that there are no students at the computer lab?

Probability of completing the planning

f$)$ What percentage of the time is the help desk busy?

g$)$ What is the probability that there are exactly $2$ students in the lab?

h$)$ By how much would your answer to part $($a$)$ be reduced if a second help desk, which could do the

same work, were added?