To find the sample mean (part a), we will calculate the average of the given GPA values for the 12 students. The GPA values provided in the image are:

$2.4, \ 3.1, \ 2.6, \ 1.9, \ 0.8, \ 4.0, \ 2.4, \ 1.5, \ 3.6, \ 0.2, \ 2.4, \ 3.4$

Formula for the sample mean:

$\bar{x} = \frac{\sum x_i}{n}$ where:

• $\bar{x}$ is the sample mean
• $\sum x_i$ is the sum of all the GPA values
• $n$ is the number of students (in this case, $n = 12$)

Let me calculate this for you.The sample mean GPA for the 12 students is $\bar{x} = 2.36$, rounded to two decimal places.

Would you like to proceed with the next parts (b) and (c) of the problem, or have further details about this part?

Here are some related questions to explore:

1. How do we calculate the variance and standard deviation for a sample?
2. What is the significance of assuming the population is normally distributed?
3. How does rounding affect the accuracy of statistical results?
4. What is the difference between a sample mean and a population mean?
5. How do you calculate confidence intervals for the sample mean?

Tip: When rounding in statistics, always be consistent with the number of decimal places across calculations to maintain accuracy.