The Poisson probability formula is shown to the right, where X is the number of times the event occurs and 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.

P(X=x)=exx!

Suppose that a hospital keeps records of emergency room traffic. These records reveal that the number of patients who arrive between

7P.M. and 8P.M. has a Poisson distribution with parameter=7.7.Complete parts a through c.