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 the items containing less than 50 parts per million ( ppm) PCM is generally not regulated . A certain kind of small capacitor contains PCB with a mean of 48.2 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 37 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. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places .

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!