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Suppose that unemployment claims per 50 square miles follow a Poisson distribution with a mean of...

Suppose that unemployment claims per 50 square miles follow a Poisson distribution with a mean of 250,000, s.d. of 50,000. We take a random sample of 500 areas of 50 square miles each. What is the probability that the average number of unemployment claims in this sample is greater than 255,000?

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