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 6000 cars. (b) The Poisson distribution can be used to approximate the binomial distribution for large values of $n$ and small values of $p .$ Repeat part (a) using a Poisson distribution and compare the results.
Added by Christine D.
Step 1
C(n, k) is the binomial coefficient, which gives the number of ways to choose k successes from n trials. In this case, p = 1/2500 = 0.0004, n = 6000, and k = 4. Plugging these values into the formula, we get: P(X=4) = C(6000, 4) * (0.0004^4) * Show more…
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