Question

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 pp 7m. 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 48.5 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 1

Solution: We are given:

We are required to find:

We are also given that a random sample of size 37 is drawn since the sample size is greater than 30, therefore, according to the central limit theorem, we can use the normal distribution to find the given probability.

Using the z-score formula, we have:

Now using the standard normal table, we have:

The excel function to find this:

Therefore, the probability that the disposal of such capacitors will be regulated is 0.192