$*$THERES ARE FOUR PARTS$**$ INCLUDED IN PROBLEM$**$ PARTS a$-$d

Problem $10-6($Algo$)$

Students arrive at the Administrative Services Office at an average of one every $6$ minutes, and their requests take, on average, $4$ 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 the student spend waiting in line?

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

d$.$ what is the probability that an ariving student $($just before entering administrative service office$)$ will find at least one other student waiting in line?