SOLUTION: Seven percent of the items produced at a factory are defective. The quality control team selects a random sample of 25 items. a. What is the probability that more than three items

Question 1025786: Seven percent of the items produced at a factory are defective. The quality control team selects a random sample of 25 items.
a. What is the probability that more than three items in the sample are defective?
b. If items are selected randomly until the first defective item is encountered, how many items, on average, will have to be sampled before the first defective item is found?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
a. Let X = # of items that are defective. The r.v. X follows the binomial distribution.
==> , to four decimal places.
b. Let X = the number of trials in getting the first defective item.
This r.v. follows the geometric distribution with support 1,2, 3, 4, 5,... .
The mean of the geometric distribution where the probability of success is p = 0.07 (in this case getting a defective item) is 1/p = 1/0.07 = 14.2857, or 14 items.
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