A quality control engineer is in charge of testing whether or not 90% of the DVD

Question

A quality control engineer is in charge of testing whether or not 90% of the DVD players produced by his company conform to specifications. To do this, the engineer randomly selects a batch of 12 DVD players from each day's production. The day's production is acceptable provided no more than 1 DVD player fails to meet specifications. Otherwise, the entire day's production has to be tested. What is the probability that the engineer incorrectly passes a day's production as acceptable if only 80% of the day's DVD players actually conform to specification?

Explanation / Answer

TOTAL DVD TO BE CHECKED = 12

TOTAL DVD HAVE TO PASS = 11

TOTAL DVD WHICH CAN FAIL = 1

TOTAL CORRECT DVD IN THE LOT = 0.80*12 = 9.6=10

THEREFORE TOTAL DVD WITHOUT CONFORMATION = 12 - 10 =2

THEREFORE THE PROBABILITY THAT THE ENGINEER WILL PASS THE DEFECTED AS ACCEPTABLE = 2/10 (TOTAL DEFECTED/ TOTAL ACCEPTABLE) = 0.20 = 20%

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