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?
A) 11.7%
B) 1.17%
C) 88.3%
D) 8.83%
E) 3.89%

Question

Quizplus · Accepted Answer

Using the normal distribution, we calculate the z-score for 80 ppm: z = (80 - 75) / 4.2 ≈ 1.19. The percentage of batches exceeding 80 ppm corresponds to the area to the right of this z-score, which is approximately 11.7%.

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