A small call center, staffed by only one operator $($server$),$ has $20$ customers calling every hour with a standard deviation of inter$-$arrival times of $3$ minutes. $($This results in

ca$^2=1.)$ The activity time for a call center operator to process each call $($by addressing the caller$$s queries$)$ is$,$ on average, $2\mathrm{.}5$ minutes with a standard deviation of $8$ minutes $($or

ce$^2=10\mathrm{.}24),$ primarily because of the wide variety of caller queries. $($Hint: Consider these processing times to be General, not Exponential.$)$

Suppose that for every minute of time a caller waits for service, the call center is required to pay out a penalty of $60$ cents. What is the estimated hourly penalty pay out by the call center for caller wait times? $($Hint: To answer this question, consider how long the average customer spends waiting in line and how many customers might arrive in an hour.$)$