We now give an example where Poisson probabilities are required.

Question: Arrival of phone calls

A homogeneous Poisson process might be used to model arrival of telephone calls in an office. We will assume that calls arrive at a constant rate of \(\lambda = 3\) per hour during the morning (8:30 am to 12:30 pm).

  1. What are the mean and standard deviation of the number of calls arriving in a single hour?
  2. What is the probability of getting three or more calls in a single hour?
  3. What is the probability of getting no calls in a 20-minute period?

(Solved in full version)