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In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the $98 \%$ confidence interval for the mean waste recycled per person per day for the population of Washington. Assume the population is approximately normat:

Step 2 of 2 : Construct the $98 \%$ confidence interval. Round your answer to one decimal place.
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Step 1 ：Given values are mean = 1.6, standard deviation = 0.43, sample size = 13, and Z-score for 98% confidence interval = 2.33.

Step 2 ：Calculate the margin of error using the formula: \(Z \times \frac{standard deviation}{\sqrt{sample size}}\).

Step 3 ：Substitute the given values into the formula to get the margin of error = 0.27787706329902856.

Step 4 ：Calculate the lower bound of the confidence interval using the formula: \(mean - margin of error\). Substitute the given values into the formula to get the lower bound = 1.3.

Step 5 ：Calculate the upper bound of the confidence interval using the formula: \(mean + margin of error\). Substitute the given values into the formula to get the upper bound = 1.9.

Step 6 ：The 98% confidence interval for the mean waste recycled per person per day for the population of Washington is \(\boxed{(1.3, 1.9)}\) pounds.