Lesson 6

Problem. Returning to the call center, suppose that an average of \(4.5\) calls are received per hour. How many operators should the call center hire? The original question remains unanswerable: both in real life and in our mathematical model, there is a nonzero probability that a very large number of calls will come in. A reasonable refinement of the question might be: what is the minimum number of operators \(m\) such that the probability of receiving more than \(m\) calls is less than \(0.1\)?

\[F(m)=\sum_{k=0}^{m}\frac{4.5^ke^{-4.5}}{k!}> 0.9 \ .\]