The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below. $\begin{array}{lll}2.5 & 3.4 & 2.7 \\ & \text { 마 }\end{array}$ Assume the population is normally distributed. $\begin{array}{llll}1.8 & 0.7 & 4.0\end{array}$ $\begin{array}{lll}2.2 & 1.3 & 3.8\end{array}$ $\begin{array}{lll}0.4 & 2.1 & 3.3\end{array}$ (a) Find the sample mean. $\bar{x}=\square$ (Round to two decimat places as needed.) (b) Find the sample standard deviation. $s=\square$ (Round to two decimal places as needed.) (c) Construct a $99 \%$ confidence interval for the population mean $\mu$. A $99 \%$ confidence interval for the population mean is ( $\square \square$ ). (Round to two decimal places as needed.)

Step 1 ：First, we calculate the sample mean by adding all the GPA values and dividing by the total number of students, which is 12.

Step 2 ：Next, we calculate the sample standard deviation. This involves subtracting the mean from each GPA value, squaring the result, adding all these squared values, dividing by the number of students minus 1, and then taking the square root of the result.

Step 3 ：Finally, to construct a 99% confidence interval for the population mean, we use the formula for a confidence interval, which is the sample mean plus or minus the product of the standard deviation, the z-score corresponding to the desired level of confidence (which is 2.576 for a 99% confidence interval), and the square root of the number of students.

Step 4 ：The sample mean is \( \boxed{2.35} \).

Step 5 ：The sample standard deviation is \( \boxed{1.17} \).

Step 6 ：The 99% confidence interval for the population mean is \( \boxed{(1.48, 3.22)} \).