Students arrive at the Administrative Services Office at an average of one every 22 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?

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 at least one student exists in waiting line?