People suffering from hypertension, heart disease, or kidney problems may need to limit their intakes of sodium. The public health departments in some US states and Canadian provinces require community water systems to notify their customers if the sodium concentration in the drinking water exceeds a designated limit. In Connecticut, for example, the notification level is 28 mg/L (milligrams per liter). Suppose that over the course of a particular year the mean concentration of sodium in the drinking water system in Connecticut is 18.6 mg/L, and the standard deviation is 6 mg/L.

Imagine that the water department selects a simple random sample of 31 water specimens over the course year. Each specimen is sent to a lab for testing, and at the end of the year the water department computes concentration across the 31 specimens. If the mean exceeds 20 mg/L, the water department notifies the p recommends that people who are on sodium-restricted diets inform their physicians of the sodium content drinking water. Use the Distributions tool to answer the following questions, adjusting the parameters as necessary.

1. Even though the actual concentration of sodium in the drinking water is within the limit, there is a probability that the water department will advise its customers of an above-limit concentration of sodium.

2. Suppose that the water department Is willng to accept (at most) a 1% risk of erroneously notifying its customers that the sodium concentration is above the limit. A primary cause of sodium in the water supply is the salt applied to roadways during the winter to melt snow and ice. If the water department can't control the use and can't change the mean or the standard deviation of the sodium concentration in the drinking water, is anything the department can do to reduce the risk of an erroneous notification to 1%?

a. It can increase its sample size to n = 33
b. No, there is nothing it can do.
c. It can increase its sample size to n = 100
d. It can increase its sample size to n = 48.