dolution

A recreational vehicle
(RV) center is planning to install a recreational vehicle wash. Because an
average RV is 20 feet long, no more than four can fit in the 85-foot driveway
that feeds into the automatic washer. The washing personnel can handle an average
of four per hour (Poisson distributed) and they expect an average of three cars
per hour to show up.

a) What will be the
average length of the line of vehicles?

b) What is the
probability that there will be no vehicles in the car wash? (CLO3:10 Marks)

6. A local bank has two
drive-thru teller windows with an essentially unlimited queue length. They
estimate that the arrival rate during their most busy time will average about
40 cars per hour. They also estimate they can serve an average of 50 cars per hour.
Management wants to make sure that the system is operating efficiently.

a) What is the
probability that there will be no cars in the system?

b) On average, how many cars are in the
system?

c) How long would a car
be waiting (in seconds) in the driveway, on average? (CLO3:10 Marks)