Atlantic Video, a small video rental store in Philadelphia, is open $24$ hours a day, and$$due to its proximity to a major business school$$experiences customers arriving around the clock. A recent analysis done by the store manager indicates that there are $40$ customers arriving every hour, with a standard deviation of interarrival times of $2$ minute$($s$).$ This arrival pattern is consistent and is independent of the time of day. The checkout is currently operated by one employee, who needs on average $1\mathrm{.}10$ minute$($s$)$ to check out a customer. The standard deviation of this checkout time is $3$ minute$($s$),$ primarily as a result of customers taking home different numbers of videos.

$($a$)$ If you assume that every customer rents at least one video $($i$.$e$.,$ has to go to the checkout$),$ what is the average time a customer has to wait in line before getting served by the checkout employee, not including the actual checkout time $($within one minute$)?$