SOLUTION: 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

Question 313647: 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 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.3 ppm and a standard deviation of 5 ppm. The Environmental Protection Agency takes a random sample of 39 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 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!
Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.3 ppm and a standard deviation of 5 ppm.
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The Environmental Protection Agency takes a random sample of 39 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 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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Draw the distribution curve for the "small cap PCB"
mean = 48.3 ; std = 5
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Find the t-value = 49.5:
t(49.5) = (49.5-48.3)/[5/sqrt(39)] = 1.4988
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Find P(t> 1.4988 when df = 38) = tcdf(1.4988,1000,38) = 0.0711
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Cheers,
Stan H.
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