1) Students arrive at the Administrative Office at an average of one every 24 minutes, and their requests take on average 12 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? (round to 2 decimal Places)
b) How much time on average, does a student spend waiting in line? (round your answer to the nearest whole number)
c) How long is the waiting line on average? (2 decimal places)
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? (4 decimal places)
2) Sharp discounts wholesale club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes. The service time at each service desk is five minutes per customer.
a) How often (percentage of time) is each service desk idle? (2 decimal places)
b) What is the probability that both service clerks are busy? (4 decimal places)
c) What is the probability that both service clerks are idle? (round 4 decimal places)
d) How many customers, on average, are waiting in line in front of each service desk? (2 decimal places)
e) How much time does a customer spend at the service desk( waiting plus service time)? Round your answer to 2 decimal places)