1. 3. An application of the sampling distribution of the sample mean People sutfering from
hypertension, heart disease, or kidney problems may need to limit their intakes of sodium. The
public health departments in some U.S. 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 28mg/L (milligrams per liter).
Suppose that over the course of a particular year the concentration of sodium in the drinking water
of a water system in Connecticut is not extremely nonnormal, with a mean of 25.8mg/L and a
standard deviation of 6mg/L. Imagine that the water department selects a simple random sample
of 31 water specimens over the course of this year. Each specimen is sent to a Iab for testing, and
at the end of the year the water department computes the mean concentration across the 31
specimens. If the mean exceeds 28 mg/L, the water department notifies the public and
recommends that people whe are on sodium-restricted diets inform their physicians of the sodium
content in their drinking water. Use the Distributions tool to answer the following questions,
adjusting the parameters as necessary. Even though the actual concentration of sodium in the
drinking water is within the limit, there is a probability that the water department will erroneously
advise its customers of an above-limit concentration of sodium.Use the Distributions tool to answer
the following questions, adjusting the parameters as necessary. Even though the actual
concentration of sodium in the drinking water is within the limit, there is a probability that the water
department will erroneously advise its customers of an above-limit concentration of sodium.
Suppose that the water department is willing 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 sait that is applied to roadways during the winter to melt snow and ice. If the
water department can't control the use of road salt and can't change the mean or the standard
deviation of the sodium concentration in the drinking water, is there anything the department can
do to reduce the risk of an erroneous notification to 1% ? No, there is nothing it can do. It can
increase its sample size to n=88. It can increase its sample size to n=40. It can increase its
sample size to n=48.