Let's solve this problem step by step.
1. Given Information:
- 30 students take exactly 1 course.
- 15 students take exactly 2 courses.
- The relative frequency for 1 course is 0.6.
2. Finding the Total Number of Students:
- To find the total number of students, we will use the relative frequency for students taking exactly 1 course. The relative frequency for 1 course is given by:
[tex]\[
\text{Relative Frequency} = \frac{\text{Number of Students Taking 1 Course}}{\text{Total Number of Students}}
\][/tex]
- Rearrange the formula to solve for the total number of students:
[tex]\[
\text{Total Number of Students} = \frac{\text{Number of Students Taking 1 Course}}{\text{Relative Frequency}}
\][/tex]
- Substituting the known values:
[tex]\[
\text{Total Number of Students} = \frac{30}{0.6} = 50
\][/tex]
3. Finding the Relative Frequency of Students Taking Exactly 2 Courses:
- The number of students taking exactly 2 courses is 15.
- The relative frequency for 2 courses is calculated as:
[tex]\[
\text{Relative Frequency for 2 Courses} = \frac{15}{50} = 0.3
\][/tex]
4. Calculating the Percentage of Students Taking Exactly 2 Courses:
- The percentage is calculated by multiplying the relative frequency by 100:
[tex]\[
\text{Percentage of Students Taking Exactly 2 Courses} = 0.3 \times 100 = 30\%
\][/tex]
- Rounded to the nearest whole number, we get:
[tex]\[
30\%
\][/tex]
5. Calculating the Percentage of Students Taking 1 or 2 Courses:
- Combine the number of students taking 1 course and 2 courses:
[tex]\[
\text{Total Students Taking 1 or 2 Courses} = 30 + 15 = 45
\][/tex]
- Calculate the percentage:
[tex]\[
\text{Relative Frequency for 1 or 2 Courses} = \frac{45}{50} = 0.9
\][/tex]
[tex]\[
\text{Percentage of Students Taking 1 or 2 Courses} = 0.9 \times 100 = 90\%
\][/tex]
- Rounded to the nearest whole number, we get:
[tex]\[
90\%
\][/tex]
Summary of Answers:
- The percentage of students who take exactly 2 courses is [tex]\(30\%\)[/tex].
- The percentage of students who take either 1 or 2 courses is [tex]\(90\%\)[/tex].
