Management of a manufacturing company has carefully screened and selected 12 doz

Question

Management of a manufacturing company has carefully screened and selected 12 dozen components, in this case a small plastic tube through which compressed air will flow, and it is agreed that the sample contains 15 nonconforming items (all for various cosmetic reasons). The tubes are classified into "good" and "bad" piles by an inspector. The inspector ends up rejecting 7 good tubes, and accepting 6 bad tubes. The inspector classifies the remaining items in the sample correctly. On average, what is the probability that this inspector will reject a tube? Enter your response rounded to three decimal places On average, what is the probability that this inspector will make a wrong decision? Enter your response rounded to three decimal places. On average, what is the proportion of accepted tubes that are actually nonconforming? Enter your response rounded to three decimal places.

Explanation / Answer

There are total 144 tubes out of which 15 are bad and 129 are good.

The inspector rejects 7 good tubes as bad, accepts 6 bad tubes as good and the rest(122 + 9) as they are.

So, tubes rejected = 7(good but rejected) + 9(bad and rejected) = 16

a. Prob of rejecting = 16/144 = 1/9

b. Wrong decisions made = 6+7 = 13

Prob of wrong decision = 13/144

c. Accepted tubes = 122 + 6 = 128

Non conforming but accepted tubes = 6

Required probability = 6/128 = 3/64

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