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Black and White Cabs uses two dispatchers to handle requests for service and dispatch the cabs....

Black and White Cabs uses two dispatchers to handle requests for service and dispatch the cabs. The telephone calls that are made to Black and White Cabs 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 40 calls per hour, and that each dispatcher can handle a mean of 30 calls per hour.

(a) (2 marks) What percentage of the time are both dispatchers idle?
(b) (2 marks) What percentage of the time are both dispatchers busy?
(c) (2 marks) What is the probability callers will receive a busy signal if three dispatchers are used?
(d) (2 marks) If the company wants at most 12% of the callers to receive a busy signal, how many dispatchers should be used?
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