Question 446289:
Central limit theorem: Sample mean
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of ppm and a standard deviation of ppm. The Environmental Protection Agency takes a random sample of of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is ppm or more. Find the probability that the disposal of such capacitors will be regulated.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than (47.5) parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of (47.5) ppm and a standard deviation of (5) ppm. The Environmental Protection Agency takes a random sample of 40 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is (48.5) ppm or more.
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Find the probability that the disposal of such capacitors will be regulated.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
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That is the probability there are >=48.5 ppm of pollutants in the
product which has a mean of 47.5 and std of 5.
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The sample of 40 says the following:
t(48.5) = (48.5-47.5)/[5/sqrt(40)] = 1.2649..
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P(x-bar >= 48.5) = P(t >= 1.2649 when df=39) = 0.1067.. or 10.67%
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Cheers,
Stan H.
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