A company's manufacturing process uses 500 gallons of water at a time.A "scrubbing" Machine then removes most of a chemical pollutant before pumping the water into a nearby Lake .To meet federal regulations the treated water must not contain more than 80 parts per Million (ppm.) of the chemical.The machine's output can be described by a normal model With standard deviation 4.2 ppm.The company's lawyers insist that not more than 2% of the Treated water should be over the limit.To achieve this, to what mean should the company set The scrubbing machine?

Question

Quizplus · Accepted Answer

To ensure no more than 2% of the treated water exceeds the 80 ppm limit, we use the normal distribution's properties. The Z-score corresponding to the top 2% is approximately 2.05 (from standard normal distribution tables). Given a standard deviation of 4.2 ppm, we calculate the mean using the formula: mean = desired limit - (Z-score * standard deviation) = 80 - (2.05 * 4.2) ≈ 71.374 ppm. This setting minimizes the risk of exceeding the limit in more than 2% of the output.

A Company's Manufacturing Process Uses 500 Gallons of Water at a Time.A