\begin{tabular}{|c|c|c|c|}
\hline
\# Courses & Frequency & \begin{tabular}{c}
Relative \\
Frequency
\end{tabular} & \begin{tabular}{c}
Cumulative \\
Frequency
\end{tabular} \\
\hline
1 & 30 & 0.6 & 0.6 \\
\hline
2 & 15 & 0.3 & 0.9 \\
\hline
3 & 5 & 0.1 & 1.0 \\
\hline
\end{tabular}

Answer the following two questions:

1. What percent of students take exactly two courses?
Round to a whole number. Do not include decimals. [tex]$\qquad$[/tex] [tex]$\%$[/tex]

2. What percent of students take one or two courses?
Round to a whole number. Do not include decimals. [tex]$\qquad$[/tex] [tex]$\%$[/tex]



Answer :

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].