Michael, the regional manager of the Scranton branch of Dunder Mifflin Paper Com
ID: 3057136 • Letter: M
Question
Michael, the regional manager of the Scranton branch of Dunder Mifflin Paper Company, recieved some complaints about the quality of their paper products. He decided to send Creed, the company's quality assurance director, to perform a quality assessment in one of their warehouses in PA. When he visited the warehouse, there were total 500 batches of paper boxes stoked. Among the 500 batches, in addition, there were 4 defective batches which contain a box (or boxes) with poor quality papers.
a).Suppose Creed randomly sampled 5 batches of paper boxes with replacement. What is the probability that he would find one defective batch? (Round the probability to four decimal places.)
b.) Suppose Creed randomly sampled the batches of paper boxes with replacement until he find the first defective batch. What would be the expected number of batches he needed to sample?
c.) 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
a)from binomial distribution
probabiliy of defective =4/500
hence probability that he would find one defective batch 5C1 (4/500)1*(496/500)4=0.0387
b) rom geometric distribution
expected number of batches he needed to sample =1/p =(1/(4/500))=125
c)from hypregeometric distribution
probability that he would find one defective batches =4C1 *496C4 /500C5 =0.0390