Question

Use the following information to answer questions 1-2.
GPA data for the 2024 Statistics class was collected. The following are the results.
GPA
Number of Students
1.00 - 1.49
5
1.50 - 1.99
13
2.00 - 2.49
20
2.50 - 2.99
27
3.00 - 3.49
25
3.50 - 4.00
7
Your answer
1. If a student is chosen at random, what is the probability that they * 10 points have a GPA between 3.00 - 3.49 OR between 3.50 - 3.99?

Answer 1

To find the probability that a randomly chosen student has a GPA between 3.00 - 3.49 or between 3.50 - 4.00, we first need to determine the total number of students and then find the number of students within each requested GPA range.

1. **Calculate the total number of students:**

- 1.00 - 1.49: 5 students
- 1.50 - 1.99: 13 students
- 2.00 - 2.49: 20 students
- 2.50 - 2.99: 27 students
- 3.00 - 3.49: 25 students
- 3.50 - 4.00: 7 students

Total number of students = 5 + 13 + 20 + 27 + 25 + 7 = 97

2. **Find the number of students with GPAs in the specified ranges:**

- Students with GPA between 3.00 - 3.49: 25
- Students with GPA between 3.50 - 4.00: 7

Total number of students with GPA between 3.00 - 3.49 or 3.50 - 4.00 = 25 + 7 = 32

3. **Calculate the probability:**

The probability \( P \) that a randomly chosen student has a GPA between 3.00 - 3.49 or 3.50 - 4.00 is given by:

\[
P = \frac{\text{Number of students in the specified GPA ranges}}{\text{Total number of students}} = \frac{32}{97}
\]

Therefore, the probability is:

\[
P \approx 0.329 (or \approx 32.9\%)
\]