Suppose that in a batch of 500 components, 20 are defective and the rest are good....

Suppose that in a batch of 500 components, 20 are defective and the rest are good. A sample of 10 components is selected at random with replacement, and tested. Let X denote the number of defectives in the sample.

a. What is the PMF of X? State the distribution, its parameters, and give the equation for its PMF with the correct parameters.

b. What is the probability that the sample contains at least one defective component?

Solutions

Expert Solution

a) This is a binomial distribution.

n = 10

p = 20/500 = 0.04

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

b) P(X > 1) = 1 - P(X = 0) = 1 - (10C0 * 0.04⁰ * 0.96¹⁰) = 0.3352

orchestra answered 1 year ago

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