The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below. Assume the population is normally distributed. $\begin{array}{lll}2.3 & 3.3 & 2.8 \\ 1.6 & 0.9 & 4.0 \\ 2.5 & 1.4 & 3.8 \\ 0.3 & 2.3 & 3.1\end{array}$ (a) Find the sample mean. $\bar{x}=\square$ (Round to two decimal places as needed.)
Solution
Step 1 ：The grade point averages (GPA) for 12 randomly selected college students are given as follows: \(2.3, 3.3, 2.8, 1.6, 0.9, 4.0, 2.5, 1.4, 3.8, 0.3, 2.3, 3.1\).
Step 2 ：We are asked to find the sample mean. The sample mean is calculated by summing all the GPA values and then dividing by the number of students.
Step 3 ：In this case, we have 12 students. So, we sum all the GPA values and divide by 12.
Step 4 ：The sum of all GPA values is \(2.3 + 3.3 + 2.8 + 1.6 + 0.9 + 4.0 + 2.5 + 1.4 + 3.8 + 0.3 + 2.3 + 3.1 = 28.3\).
Step 5 ：Dividing this sum by the number of students, we get the sample mean as \(\frac{28.3}{12} = 2.358333333333334\).
Step 6 ：Rounding this to two decimal places, we get the final answer.
Step 7 ：The sample mean is \(\boxed{2.36}\).
