According to the IRS, 1.1% of tax returns will be audited next year. A random sample of 40 tax returns was selected. Use the Poisson distribution to approximate the binomial distribution to determine the probability that more than two of these tax returns will be audited.

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Quizplus · Accepted Answer

The Poisson distribution can approximate the binomial distribution when the probability of success is small and the number of trials is large. Here, λ = np = 40 * 0.011 = 0.44. The probability of more than two audits is 1 - P(X ≤ 2), which is approximately 0.0726 using the Poisson distribution.