A help desk in the computer lab serves students on a first$-$come, first served basis. On average, $15$ students need help

every hour. The help desk can serve an average of $20$ students per hour.

Based on this description, we know:

$\backslash$mu $=20$ students$/$hour $($average service time is $3$ minutes$)$

$=15$ students$/$hour $($average time between student arrivals is $4$ minutes$)$

Answer the following $($MUST show all steps and formulas to receive any credit$)$:

$1.$ Utilization factor for the system

$2.$ Average number of students $($AKA units$)$ in the system, $($waiting plus being served$)$

$3.$ Average time a student $($AKA unit$)$ spends waiting in system, $($waiting plus service time$)$

$4.$ Average number of students $($AKA units$)$ waiting in the queue

$5.$ Average time student $($AKA unit$)$ spends waiting in the queue

$6.$ Probability of $0$ students $($AKA units$)$ in the system $($that is$,$ the service is idle$)$