Unit $8$ Exercises

Question $8\mathrm{.}1$

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?