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.$)$

Based on the information above, what percentage of the time will the staff member be busy? $($If your answer is $15\mathrm{.}7\%,$ please enter $15\mathrm{.}7,$ not $0\mathrm{.}157)$