Problem $7-15($Algo$)$

Students arrive at the Administrative Services Office at an average of one every $20$ minutes, and their requests take, on average, $15$

minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume

Poisson arrivals and exponential service times.

a$.$ What percentage of time is Judy idle?

Note: Round your answer to $1$ decimal place.

Answer is complete but not entirely correct.

b$.$ How much time, on average, does a student spend waiting in line?

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

Answer is complete and correct.

$45\mathrm{.}0$

c$.$ How long is the $($waiting$)$ line on average?

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

Answer is complete and correct.

d$.$ What is the probability that an arriving student $($just before entering the Administrative Services Office$)$ will find at least one other

student waiting in line?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Answer is complete but not entirely correct.

$0\mathrm{.}561\%$