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.(Use binomial probability)

What is the probability that a random sample of 30 sales has less than four returns?

What is the probability that the number of returns is not equal to 4 in a random sample of 30 sales?

What is the probability that a random sample of 30 sales has more than three returns?

Answer 1

n = 30

p = 0.04

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X < 4)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 30C0 * (0.04)^0 * (0.96)^30 + 30C1 * (0.04)^1 * (0.96)^29 + 30C2 * (0.04)^2 * (0.96)^28 + 30C3 * (0.04)^3 * (0.96)^27

= 0.9694

b) P(X 4) = 1 - P(X = 4)

                   = 1 - (30C4 * (0.04)^4 * (0.96)^26)

                   = 1 - 0.0243 = 0.9757

c) P(X > 3) = 1 - P(X < 3)

                  = 1 - (30C0 * (0.04)^0 * (0.96)^30 + 30C1 * (0.04)^1 * (0.96)^29 + 30C2 * (0.04)^2 * (0.96)^28 + 30C3 * (0.04)^3 * (0.96)^27)

                  = 1 - 0.9694

                  = 0.0306