Last year, a manufacturer produced 1,950,000 DVD players. Of these, approximately 5% were defective. Assume that a simple random sample of n = 230 players is drawn. Use the Poisson Approximation to the binomial distribution to compute the probability that exactly nineteen of the 230 DVD players were defective.

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Quizplus · Accepted Answer

The Poisson approximation to the binomial distribution is given by:P(X = k) = (e^-λ * λ^k) / k!where λ = npIn this case, n = 230 and p = 0.05, so λ = 11.5P(X = 19) = (e^-11.5 * 11.5^19) / 19! = 0.0119

Last Year, a Manufacturer Produced 1,950,000 DVD Players