A library has a single reference desk that provides research assistance to students. On average, $10$ students

arrive per hour at the desk. The reference librarian can help $12$ students in an hour. Due to variability in the

arrivals, the average number of students waiting in line is $1\mathrm{.}8$ students. You must use the notation $($i$.$e$.,$

letters defined for each$)$ taught in class, or a zero grade will be assigned to this question.

Compute the following $($Hint: Little$$s Law works for any system$/$sub$-$system: for the whole system

including line and server combined, for the line only, and for the server only$)$:

$($a$)$ The utilization of the reference desk

$($b$)$ The average number of students in the system

$($c$)$ The average time a student spends waiting in line

$($d$)$ The average time a student spends in the system.