A clinic is equally likely to have 2, 3, or 4 doctors volunteer for service on a given day. No matter how many volunteer doctors there are on a given day, the numbers of patients seen by these doctors are independent Poisson random variables with mean 30. Let X denote the number of patients seen in the clinic on a given day.
(a) Find E[X].
(b) Find Var(X).
(c) Use a table of the standard normal probability distribution to approximate P{X > 65}.
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