Problem $10-6($Algo$)$

Students arrive at the Administrative Services Office at an average of one every $12$ minutes, and their requests take, on average, $8$ 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.

Percentage of time

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.

Average time

minutes

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

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

Average length of the waiting line

students

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 $4$ decimal places.