Calls arrive at James Hamann’s hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and exponential distributions appear to be relevant in this situation.

(a) What is the probability that the operator is busy?

(b) What is the average time that a customer must wait before reaching the operator?

(c) What is the average number of calls waiting to be answered??’