1.) Which of the following best describes the expected value of a discrete random variable?

a. It is the geometric average of all possible outcomes.

b. It is the weighted average over all possible outcomes.

c. It is the simple average of all possible outcomes.

d. None of the above

(topic is MULTIPLE-CHANNEL WAITING LINE

MODEL WITH POISSON ARRIVALS AND

EXPONENTIAL SERVICE TIMES)

NOTE! use this given situation to answer numbers 2 to 6

A Florida coastal community experiences a population increase during the winter months with seasonal residents arriving from northern states and Canada. The post office counter has three work stations. The service rate of each postal clerk is 0.75 customer per minute. The anticipated arrival rate is 1.2 customers per minute. Assume that customer arrivals follow a Poisson probability distribution, with an arrival and that service times follow an exponential probability distribution.

2.) Determine the probability that no customers are in the system

a. 35/187

b. 1024/3927

c. 2048/6545

d. 256/935

3.) Determine the average number of customers waiting

a. 35/187

b. 1024/3927

c. 2048/6545

d. 256/935

4.) Determine the average number of customers in the system

a. 0.2737

b. 0.2608

c. 0.1942

d. 1.9129

5.) Determine the average time a customer spends in the system

a. 0.2737

b. 1.5941

c. 0.1942

d. 1.9129

6.) Determine the probability that arriving customers will have to wait for service

a. 0.2737

b. 1.5941

c. 0.1942

d. 1.9129