07 ION 8-2 Union, Intersection, and Complement of Events; Odds 76. Quality contr

Question

07 ION 8-2 Union, Intersection, and Complement of Events; Odds 76. Quality control. An assembly plant produces 40 outboard motors, including 7 that are defective. The quality control department selects 10 at random (from the 40 produced) for testing and will shut down the plant for trouble shooting if 1 or more in the sample are found to be defective. What is the probability that the plant will be shut down? 77. Medicine. In order to test a new drug for adverse reactions the drug was administered to 1,000 test subjects with the following results: 60 subjects reported that their only adverse reaction was a loss of appetite, 90 subjects reported that their only adverse reaction was a loss of sleep, and 800

Explanation / Answer

Number of motors = 40

Number of defective motors = 7

P(motor is defective) = 7/40 = 0.175

P(motor is working fine) = 1 - 0.175 = 0.825

Plant will shut down if one or more motors are faulty

P(Plant will not shut down) = 10C0 * (0.825)^(10) * (0.175)^0 = 0.1460

P(plant will shut down) = 1 - P(plant will not shut down) = 1 - 0.1460 = 0.839

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