Suppose that an automobile parts wholesaler claims that .5 percent of the car batteries in a shipment are defective. A random sample of 200 batteries is taken, and four are found to be defective.
a. Use the Poisson approximation discussed in Exercise 5.37 to find the probability that four or more car batteries in a random sample of 200 such batteries would be found to be defective, if we assume that the wholesaler's claim is true.
b. Based on your answer to part a, do you believe the claim? Explain.