Question: SLICE NAME Random Variables and Distributions TOPIC NAME Central limit theorem: Sample mean Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in

SLICE NAME Random Variables and Distributions

TOPIC NAME 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 than50parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of48.3ppm and a standard deviation of8ppm. The Environmental Protection Agency takes arandom sampleof39of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is49

ppm or more.

Find the probability that the disposal of such capacitors will be regulated.

Carry the intermediate computations to at least four decimal places. Round the answer to at least three decimal places.

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