Problem:
Students arrive at the Administrative Services Office at an average of one every 16 minutes, and their requests take on average 10 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.
Required:
Question 1) What percentage of time is Judy idle?
Question 2) How much time, on average, does a student spend waiting in line?
Question 3) How long is the (waiting) line on average?
Question 4) 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?
Solve the given numerical problem and illustrate step by step calculation.