In a shipment of 100 parts, 4 are defective. The purchaser has time to test only 10 randomly selected parts for defects. Let X be the number of defective parts the purchaser finds. (a) Give the support X of X. (b) What is the probability that the purchaser finds no defective parts? (c) What is the probability that the purchaser finds at least 1 defective part? (d) Suppose the shipment has d defective parts. What is the largest value of d such that the probability is at least 0.90 that the purchaser finds no defects among 10 randomly sampled parts?
In a shipment of 100 parts, 4 are defective. The purchaser has time to test only 10 randomly selected parts for defects. Let X be the number of defective parts the purchaser finds.
(a) Give the support X of X.
(b) What is the
(c) What is the probability that the purchaser finds at least 1 defective part?
(d) Suppose the shipment has d defective parts. What is the largest value of d such that the probability is at least 0.90 that the purchaser finds no defects among 10 randomly sampled parts?
Let denotes the number of defective parts found by the purchaser. Then, X follows hypergeometric distribution with .
The PMF of hypergeometric distribution is given by:
for
Using this PMF the required probability is determined.
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