3. Micheal, the regioual manager of the Scrauton branch of Dunder Miflin Paper C

Question

3. Micheal, the regioual manager of the Scrauton branch of Dunder Miflin Paper Compauy. received some complaints about the quality of their paper products. He decided to sen Creed, company's quality assurance director, to perform a quality assessment in oue o paper boxes stoked. which contain a box (or boxes) with poor quality papers. e were total 500 batches of Among the 500 batches, in addition, there were 4 defective batches a) (5 points) Suppose Creed randomly sampled 5 batches of paper boxes with re placement. What is the the probability that he would find one defective batch? (Round the probability to four decimal places.) (b) (5 points) Suppose Creed randomly sampled the batches of paper boxes with re- placement until he find the first defective batch. What would be the expected number of batches he needed t sample? (c) (5 points) Suppose Creed randomly sampled 5 batches of paper boxes without replacement. What is the probability that he would find one defective batches? (Round the probability to four decimal places.)

Explanation / Answer

Solution

(a) n = 500 defective batch = 4

p = 4/500 = 0.008

n = 5

Let X be the defective batch

P(x=1) = (0.008)(1-0.008)5-1 = 0.0077

(b) n = (1)(1-0.008)/(0.008) = 124

(c) P(x=1) = 5C1(0.008)(1-0.008)5-1 = 0.0387

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