Question

The Telektronic Company purchases large shipments of fluorescent bulbs and uses this acceptance-sampling plan: Randomly select and test 20 bulbs, then accept the whole batch if there is only one or none that doesn’t work. If a particular shipment of thousands of bulbs actually has a 4.5% rate of defects, what is the probability that this whole shipment will be accepted? [Assume a binomial probability distribution.]

Answer 1

p = 0.045

n = 20

This is a binomial distribuiton

P(X = x) = 20Cx * 0.045^x * (1 - 0.045)^20-x

P(shipment will be accepted) = P(X < 1)

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

                                               = 20C0 * 0.045⁰ * 0.955²⁰ + 20C1 * 0.045¹ * 0.955¹⁹

                                               = 0.7734