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 47.5 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 ppm or more. Find the probability that the disposal of such capacitors will be regulated.
The solution uses hypothesis testing of a sample of PCB capacitors to test for the probability of regulation.