Question

The probability that a DVD player produced by VCA Television is defective is estimated to be 0.04. A sample of ten players is selected at random. (Round your answers to four decimal places.) (a) What is the probability that the sample contains no defective units? (b) What is the probability that the sample contains at most two defective units?

Answer 1

p = 0.04

n = 10

This is a binomial distribution.

P(X = x) = 10Cx * 0.04^x * (1 - 0.04)^10-x

a) P(X = 0) = 10C0 * 0.04⁰ * 0.96¹⁰ = 0.6648

b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 10C0 * 0.04⁰ * 0.96¹⁰ + 10C1 * 0.04¹ * 0.96⁹ + 10C2 * 0.04² * 0.96⁸

                  = 0.9938