The Poisson probability formula is shown to the right, where X is the number of times the event occurs and λ is a parameter equal to the mean of X. This distribution is often used to model the frequency with which a specified event occurs during a particular period of time.
Suppose that a hospital keeps records of emergency room traffic. These records reveal that the number of patients who arrive between 7 P.M. and 8 P.M. has a Poisson distribution with parameter λ = 6.1.
Determine the probability that, on a given day, the number of patients who arrive at the emergency room between 7 P.M. and 8 P.M. is between 4 and 6, inclusive. P(4 ≤ X ≤ 6) =