Jeremy sells a magazine which is produced in order to raise

Jeremy sells a magazine which is produced in order to raise money for homeless people. The probability of making a sale is, independently, 0.09 for each person he approaches. Given that he approaches 40 people, and let X be the random variable that represents at most 5 sales. Find, a. the distribution of X. b. the expected and variance of X.

Solution

Given n = 40; X = 5; p=0.09 and q = 1-p = 1-0.09 = 0.91

a) The distribution X is binomial distribution asn is finnite and there are only two outcomes

b) expected value is given by mean = np =40*0.09=3.6 and

variance = npq = 3.276