$7\mathrm{.}5$ pts

$3.$ The Gem $($TG$)$ is an organic juice bar located in Philadelphia. TG is particularly famous for its protein$-$smoothies and currently has two smoothie$-$makers $($each is operated by a single employee$).$ Customers arrive at TG with an average rate of $60$ customers$/$hour$,$ and the standard deviation of inter$-$arrival times is $2$ minutes. Furthermore, historical data indicates that the protein$-$smoothie preparation times are distributed exponentially with a standard deviation of $96$ seconds.

$($a$)$ What is the average customer waiting time? $($In line$)(3\mathrm{.}5$ points$)$

$($b$)$ What is the average number of customers in TG$?($Both in line and in front of the smoothiemaker$)(2$ points$)$

$($c$)$ Manager of TG wants to decrease average customer waiting time $($in line$)$ below $5$ minutes. For that purpose, he plans to eliminate any variability in service times by switching old smoothiemakers with the new ones $($average service time will stay the same$).$ Can he reach his goal? Explain. $(2$ points$)$