# Statistical Inference - Poisson Distribution ?

Emergency Room Trafﬁc Desert Samaritan Hospital keeps records of emergency room (ER) trafﬁc. Those records indicate that the number of patients arriving between 6:00 P.M. and 7:00 P.M. has a Poisson distribution with parameter λ =6.9. Determine the probability that, on a given day, the number of patients who arrive at the emergency room between 6:00 P.M. and 7:00 P.M. will be

a. exactly 4.

b. at most 2.

c. between 4 and 10, inclusive.

d. Obtain a table of probabilities for the random variable X, the number of patients arriving between 6:00 P.M. and 7:00 P.M. Stop when the probabilities become zero to three decimal places.

e. Use part (d) to construct a (partial) probability histogram for X.

f. Identify the shape of the probability distribution of X.

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