An automobile manufacturer finds that 1 in every

2500

automobiles produced has a particular manufacturing defect.

(a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of

7000

cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p. Repeat (a) using a Poisson distribution and compare the results.

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Part 1

(a) The probability using the binomial distribution is

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.