Suppose that in a batch of 1000 rivets used in steel construction, 15 are defective. Let X be the number of defective rivets in a simple random sample without replacement of 7 from this batch. a. What is the exact probability distribution of X? Identify the distribution and give the values of all relevant parameters. b. The probability of getting exactly 1 defective rivet in the sample is 0.09645. Use the binomial distribution to find the approximate probability of getting exactly 1 defective rivet in the sample.

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