A small town with one hospital has $3$ ambulances to supply ambulance service. Requests for ambulances during nonholiday weekends average $0\mathrm{.}60$ per hour and tend to be Poisson$-$distributed. Travel and assistance time averages $2\mathrm{.}00$ hours per call and follows an exponential distribution Use

a$.$ Find system utilization. $($Round your answer to the nearest whole percent.$)$

System utilization

$\%$

b$.$ Find the average number of customers waiting. $($Round your answer to $3$ decimal places.$)$

Average number of customers

c$.$ Find the average time customers wait for an ambulance. $($Round your answer to $3$ decimal places.$)$

Average time hour

d$.$ Find the probability that all ambulances will be busy when a call comes in$.($Round intermediate calculations to $3$ decimal places and final answer to $2$ decimal places.$)$

Probability