The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 1.7 gallons. The mean water usage per family was found to be 15.7 gallons per day for a sample of 1454 families. Construct the $98 \%$ confidence interval for the mean usage of water. Round your answers to one decimal place.

Step 1 ：We are given that the sample mean (\(\bar{x}\)) is 15.7 gallons, the population standard deviation (\(\sigma\)) is 1.7 gallons, and the sample size (\(n\)) is 1454 families.

Step 2 ：We are asked to construct a 98% confidence interval for the mean usage of water. The Z-score for a 98% confidence interval is approximately 2.33.

Step 3 ：We use the formula for a confidence interval for a population mean, which is \(\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}\).

Step 4 ：Substituting the given values into the formula, we get \(15.7 \pm 2.33 \frac{1.7}{\sqrt{1454}}\).

Step 5 ：Calculating the margin of error, we get approximately 0.1039.

Step 6 ：Subtracting and adding the margin of error from the sample mean, we get the lower and upper limits of the confidence interval, which are approximately 15.6 and 15.8 respectively.

Step 7 ：Final Answer: The 98% confidence interval for the mean usage of water is \(\boxed{(15.6, 15.8)}\) gallons per day.