Question

Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components. From the shipment you take a random sample of 25. When sampling with replacement (so that the p = probability of success does not change), note that a success in this case is selecting a defective part. In our sample of 25 we reject the entire shipment if X>5. What is the probability of rejecting the entire shipment?

Answer 1

p = 68 / 400 = 0.17

n = 25

This is a binomial distribution.

P(X = x) = 25Cx * 0.17^x * (1 - 0.17)^25-x

P(X > 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))

               = 1 - (25C0 * 0.17⁰ * 0.83²⁵ + 25C1 * 0.17¹ * 0.83²⁴ + 25C2 * 0.17² * 0.83²³ + 25C3 * 0.17³ * 0.83²² + 25C4 * 0.17⁴ * 0.83²¹ + 25C5 * 0.17⁵ * 0.83²⁰ )

             = 1 - 0.7575

             = 0.2425