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Ocala Software Systems operates a technical support center for its software customrs. If customers have problems installing or using Ocala software products, then they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and told that a consultant will provide assistance as soon as possible and that customers will be served in the order that calls are received. Incoming calls follow a poisson probabiltiy distribution with an average rate of 9 calls per hour. The service time follows an exponential probability distribution, and, on average, it takes 5 minutes for a consultant to answer a customer's questions.
a. On average, how many customers will be waiting to speak to the consultant?
b. What is the average time, in minutes, that it takes for a customer to get through the system?
c. What percentage of the time is the consultant idle?
d. What is the probability that there is more than one customer in line, waiting to be helped?