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?

2. What is the complement of the question in number 1( write in words), and what is the e probability of the complement?

Answer 1

To answer the questions, we first need to calculate the total number of students and then use this to calculate probabilities.

### Total Number of Students
Let's add up the number of students in each GPA range:
- 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

Total = 5 + 13 + 20 + 27 + 25 + 7 = **97 students**

### Question 1
We want to find the probability that a student has a GPA between **3.00 - 3.49** OR between **3.50 - 4.00**.

Number of students in each GPA range:
- 3.00 - 3.49: 25
- 3.50 - 4.00: 7

Total number of students in the specified ranges:
25 + 7 = **32 students**

Now, we can find the probability:
\[
P(\text{GPA between 3.00 - 3.49 or 3.50 - 4.00}) = \frac{\text{Number of students in these ranges}}{\text{Total number of students}} = \frac{32}{97}
\]

Thus, the probability is \( \frac{32}{97} \).

### Question 2
The complement of the event in Question 1 is that a student does **not** have a GPA between **3.00 - 3.49** or between **3.50 - 4.00**.

In words, the complement is:
- "A student has a GPA less than 3.00 or greater than 4.00."

To find the probability of this complement event:
1. First, calculate the number of students not in the specified GPA ranges:
- Total students = 97
- Students with GPA between 3.00 - 4.00 = 32
- Students not in these ranges = 97 - 32 = **65 students**

Now, we can find the probability of the complement:
\[
P(\text{Not GPA between 3.00 - 3.49 or 3.50 - 4.00}) = \frac{\text{Number of students not in these ranges}}{\text{Total number of students}} = \frac{65}{97}
\]

Thus, the probability of the complement is \( \frac{65}{97} \).

### Summary
1. Probability of having a GPA between 3.00 - 3.49 or 3.50 - 4.00: \( \frac{32}{97} \)
2. Complement: "A student has a GPA less than 3.00 or greater than 4.00." Probability of the complement: \( \frac{65}{97} \)