# Calculations with Poisson and exponential distributions

Calls arrive at Lynn Ann fish'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 us 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?

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D.6 Calls arrive at Lynn Ann fish'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 ...

#### Solution Summary

This solution answers questions with Poisson and exponential distributions. The probability that an operator of a hotel switchboard is busy is determined. The average time that a customer must wait before reaching the operator is given. The average number of calls waiting to be answered is given. The expert provides equations for a step by step solution.