When a survey calls residential telephone numbers at random

When a survey calls residential telephone numbers at random, only 26% of the calls reach a live person. You watch the random dialing machine make 17 calls.

(a) What is the probability that exactly 3 calls reach a person?
(Use 3 decimal places.)

(b) What is the probability that 3 or fewer calls reach a person?
(Use 3 decimal places.)

Solution

This is a binomial distribution.

Let N be the number of live persons contacted among the 17 calls observed.

Then N has the binomial distribution with n = 17 and p = 0.26

(a) P(N = 3) = (17C3)(0.26)³(0.74)¹² = 0.1764.

(b) P(N 3) = P(N = 0) + P(N = 1) + P(N = 2) + P( N = 3) = 0.3186