Rockwell Electronics Corporation retains a

service crew to repair machine breakdowns that oc$-$

$\text{'}$

cur on an average of A $=3$ per day $($approximately Poisson in nature$).$

The crew can service an average of $\backslash$mu $=8$ machines per day, with a repair time distribution that

resembles the exponential distribution.

$($a$)$ What is the utilization rate of this service sys$-$

tem?

$($b$)$ What is the average downtime for a machine

that is broken? $$ d $().$ting to be serv$1$ce

c How many machines are wai at any given time?

$($d$)$ What is the probability that mor:.~;n;:~more machine is in the system? p~~ba t~ :erepaired

than two are broken and wait.tni! $?$ More than or being serviced? More tban t ee $$

four?