You must estimate the mean temperature (in degrees Fahrenhelt) with the following sample temperatures:
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Find the $98\mathrm{\%}$ confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).
$$98\mathrm{\%}\text{ C. }.=$$

Step 1 ：Given the sample temperatures are 73.8, 75.7, 81.3, 75.1, 75.2, 52.8, 67.8, 57.7, 64.1, 87.7, 84.3, 82.5.

Step 2 ：Calculate the sample mean, which is the sum of all sample temperatures divided by the number of samples. The sample mean is approximately 73.17.

Step 3 ：Calculate the sample standard deviation, which is a measure of the amount of variation or dispersion of the set of values. The sample standard deviation is approximately 10.74.

Step 4 ：The sample size, denoted as $n$, is the number of observations in a sample. In this case, $n=12$.

Step 5 ：Find the Z-score for a 98% confidence level. The Z-score is a measure of how many standard deviations an element is from the mean. The Z-score for a 98% confidence level is approximately 2.33.

Step 6 ：Calculate the confidence interval using the formula: $(\text{mean}-\text{Z-score}\times \frac{\text{standard deviation}}{\sqrt{n}},\text{mean}+\text{Z-score}\times \frac{\text{standard deviation}}{\sqrt{n}})$. The confidence interval is approximately $(65.96,80.38)$.

Step 7 ：$\boxed{{\displaystyle \text{The 98\% confidence interval for the mean temperature is approximately (65.96, 80.38).}}}$