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

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.
A. What percent of the batches of water discharged exceed the 80 ppm standard?
b. 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? Assume the standard deviation does not change.