Cairo Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Cairo Cab use a common telephone number. When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed. Callers who receive a busy signal can call back later or call another cab service. Assume that the arrival of calls follows a Poisson probability distribution, with a mean of 35 calls per hour, and that each dispatcher can handle a mean of 23 calls per hour.

REQUIRED:

a. What percentage of time are both dispatchers idle?

(In fraction form, example: 2/5)

b. What percentage of time are both dispatchers busy?

(In fraction form, example: 2/5)

c. What is the probability that callers will receive a busy signal if three dispatchers are used?

(In 4 decimal places)

d. What is the probability that callers will receive a busy signal if four dispatchers are used?

(In 4 decimal places)

e. If management wants no more than 12% of the callers to receive a busy signal, how many dispatchers should be used?

(In whole number)