Possion distribution with parameter 16. Find P(X>24)?

Question

A switchboard can handle only 24 phone calls per minute .If the incoming calls per minute follows a Poison distribution with parameter 16, find the probability that the switchboard is overloaded in any one minute??

Answer 1

The probability of 24 or less calls is the sum of the Poisson density from 0 to 24.

The probability of more than 24 calls is 1 - the above probability.

You may know of a computer source of Poisson probabilities; otherwise, many standard textbooks have tables.