You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
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Find the 99\% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.
$$99\mathrm{\%}\text{ C.I. }=$$

Step 1 ：Given the sample temperatures in degrees Fahrenheit: 43.1, 44.9, 52.9, 47.1, 78.5, 55.2, 56.3, 53.5, 67.9, 60.9, 69.6, 79.3.

Step 2 ：We need to find the 99% confidence interval for the mean temperature. The formula for the confidence interval is $\overline{x}\pm z\frac{s}{\sqrt{n}}$, where $\overline{x}$ is the sample mean, $z$ is the z-score (for a 99% confidence interval, $z=2.576$), $s$ is the sample standard deviation, and $n$ is the sample size.

Step 3 ：First, calculate the sample mean ($\overline{x}$) and the sample standard deviation ($s$). The sample mean is approximately 59.1 and the sample standard deviation is approximately 12.32.

Step 4 ：The sample size ($n$) is 12, as there are 12 temperatures in the sample.

Step 5 ：Substitute these values into the formula for the confidence interval: $59.1\pm 2.576\frac{12.32}{\sqrt{12}}$.

Step 6 ：Solving this gives the 99% confidence interval for the mean temperature as approximately $(49.938,68.262)$.

Step 7 ：$\boxed{{\displaystyle \text{Final Answer: The 99\% confidence interval for the mean temperature is }(49.938,68.262)}}$