Problem $7-21($Algo$)$

Benny the Barber owns a one$-$chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of $4\mathrm{.}0$ per hour. It will take Benny an average of $13$ minutes to give a haircut. Based on these figures, find the following:

a$.$ The average number of customers waiting.

Note: Round your intermediate calculations to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places and final answer to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.

Average number of customers waiting

b$.$ The average time a customer waits.

Note: Round your answer to $2$ decimal places.

Average waiting time

minutes

c$.$ The average time a customer is in the shop.

Note: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place. minutes

d$.$ The average utilization of Benny's time.

Note: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place.

Average utilization