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.Because a fine is charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water.The machine's output can be described by a normal model with standard deviation 4.2 ppm.What percent of the batches of water discharged exceed the 80 ppm standard?

Question

Quizplus · Accepted Answer

Using the normal distribution, we calculate the z-score for 80 ppm: z = (80 - 75) / 4.2 ≈ 1.19. Looking up this z-score in a standard normal distribution table, we find that approximately 88.3% of the data falls below this z-score, meaning 11.7% exceeds it.

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