Question

Emergency 911 calls to a small municipality in Idaho come in at the rate of one every two minutes. Assume that the number of 911 calls is a random variable that can be described by the Poisson distribution.

(a)	What is the expected number of 911 calls in one hour?
	per hour
(b)	What is the probability of three 911 calls in five minutes? If required, round your answer to four decimal places.
(c)	What is the probability of no 911 calls during a five-minute period? If required, round your answer to four decimal places.

Answer 1

Here there are one call every two minutes so here distribution of number of 911 calls is described by the Poisson distribution

(a) Expected number of calls in one hour = 60/2 = 30

(b) Expected number of calls in five minutes = 5/2 = 2.5

Pr(x = 3) = POISSON (x = 3 ; 2.5) = e^-2.5 2.5³ /3! = 0.2138

(c) Pr(x = 0) = POISSON (x = 0; 2.5) = e^-2.5 = 0.0821