Please select the best answer and click submit The Water Dep

Please select the best answer and click \"submit.\" The Water Department checks the city water supply on a regular basis for contaminants such as trihalomethanes (THMs). The Water Department takes 200 samples and estimates that the concentration of THMs in your drinking water is 3 ppb (parts per billion), with a standard deviation of 0.3 ppb. Assuming the samples were random and unbiased, how much confidence can you have in this data? 97% confident the average concentration of PCBs in the water supply is between 2.6 ppb and 3.8 ppb. 95% confident the average concentration of PCBs in the water supply is between 2.4 ppb and 3.6 ppb. 68% confident the average concentration of PCBs in the water supply is between 2.9 ppb and 3.1 ppb. 99.7% confident the average concentration of PCBs in the water supply is between 2.7 ppb and 3.3 ppb.

Solution

From the graph of the standard Normal Distribution,

99.7% of data lies within 3 standard deviation around the mean

95% of data lies within 2 standard deviation around the mean

68% of data lies within 1 standard deviation around the mean

The mean is 3 ppb and standard deviation is 0.3 ppm. From the above,

99.7% of data lies within (3-0.3(3))=2.1 ppb to (3+0.3(3))=3.9 ppb

95% of data lies within (3-0.3(2))=2.4 ppb to (3+0.3(2))=3.6 ppb

68% of data lies within (3-0.3(1))=2.7 ppb to (3+0.3(1))=3.3 ppb

Comparing the given options with the above calculations the answer is Option B