Last year, a manufacturer produced 1,050,000 DVD players. Of these, approximately 4% were defective. Assume that a simple random sample of n = 210 players is drawn. Use the Poisson approximation to the binomial distribution to compute the mean number of DVD players that were defective

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Quizplus · Accepted Answer

The mean ($\lambda$) of a Poisson distribution can be approximated in this context by multiplying the total number of DVD players produced (1,050,000) by the probability of a player being defective (4% or 0.04). This gives $\lambda = 1,050,000 \times 0.04 = 42,000$ defective DVD players in total. However, since we are interested in the mean number of defective players in a sample of 210, we scale this mean proportionally to the sample size: $42,000 \times \frac{210}{1,050,000} = 8.4$.

Last Year, a Manufacturer Produced 1,050,000 DVD Players