A company purchases shipments of computer components and uses the following acce

Question

A company purchases shipments of computer components and uses the following acceptance sampling plan: Randomly select and test 30 components; accept the whole batch if there are fewer than 3 defective components. A particular shipment of thousands of components actually has a 6% rate of defects.

(a) How many defective components do you expect to see among those selected?

(b) What is the probability that this whole shipment will be rejected?

(c) What is the probability that in the sample of the 30 he selects there will be least one but fewer than six defective components?

(d) What is the probability that exactly one fth of the selected components will be defective

Explanation / Answer

answer

Since we don't have the total number of components, let's work with the sampling.

With each sample, there is a 97/100 chance that the part will be acceptable. Since 27 of these successes have to happen in a sample of 30, the probability that you'll take the entire shipment is
97/100 * 97/100 * 97/100 ... 27 times
or
97^27 / 100^27

or 44%

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