Students arrive at the Administrative Services Office at an average of one every $10$ 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?

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

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

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?