Sure! Let's go through each question step-by-step:
### 1. What is the probability that a randomly selected student will study for one to two hours?
From the table, we see that the number of students who study for one to two hours is 29 out of a total of 130 students. The probability of a student studying for one to two hours is calculated as follows:
[tex]\[
\text{Probability} = \left( \frac{\text{Number of students studying 1-2 hours}}{\text{Total number of students}} \right) \times 100
\][/tex]
[tex]\[
\text{Probability} = \left( \frac{29}{130} \right) \times 100 \approx 22\%
\][/tex]
### 2. What is the probability that a randomly selected student will study more than three hours and earn a 71 to 90?
From the table, we find that the number of students who study more than three hours and earn a 71 to 90 is 18 out of a total of 130 students. The probability of a student studying more than three hours and earning a 71 to 90 is:
[tex]\[
\text{Probability} = \left( \frac{\text{Number of students studying >3 hours and earning 71-90}}{\text{Total number of students}} \right) \times 100
\][/tex]
[tex]\[
\text{Probability} = \left( \frac{18}{130} \right) \times 100 \approx 14\%
\][/tex]
### 3. What is the probability that a randomly selected student will earn a 91-100 given they study for two to three hours?
From the table, we see that the number of students who study for two to three hours and earn a 91-100 is 22. The total number of students who study for two to three hours is 45. Therefore, the conditional probability of earning a 91-100 given they study for two to three hours is:
[tex]\[
\text{Probability} = \left( \frac{\text{Number of students studying 2-3 hours and earning 91-100}}{\text{Total number of students studying 2-3 hours}} \right) \times 100
\][/tex]
[tex]\[
\text{Probability} = \left( \frac{22}{45} \right) \times 100 \approx 49\%
\][/tex]
### Summary:
- Probability that a randomly selected student will study for one to two hours is 22
- Probability that a randomly selected student will study more than three hours and earn a 71 to 90 is 14
- Probability that a randomly selected student will earn a 91 - 100 given they study for two to three hours is 49
These probabilities are 22%, 14%, and 49%, respectively.
