Question

Big Box Store (BBS) has an annual rate of 4% of all sales being returned. In a recent sample of thirty randomly selected sales the number of returns was five. BBS is concerned about the event, and your advice is solicited. (9) What is the probability that a random sample of 30 sales has more than three returns?

Answer 1

Consider X be a random variable which follows binomial distribution. The sample size, n is 30 and the probability of success, p is 0.04. The probability mass function of the binomial distribution is given by: P(X = x)= "Cp(1- p)*** The probability that a random sample of 30 sales has more than three returns is, P(X > 3)=1-(P(X =0) + P(X =1) + P(X = 2) + P( X = 3)) - C,0.04° (1-0.04)30-0 + 30C, 0.04- (1 -0.04)30-1) +3°C, 0.04(1 -0.04)30-2 + 0 0.04 (1 -0.04) 30-3) =1-(0.2938 +0.3673+0.2219+0.0863) = 0.0307