To answer the given questions, we need to complete the table and find the percentage of students taking exactly one course. Here, the total number of students surveyed is 50.
### Part (a): Completing the Table
#### Step 1: Calculate the Relative Frequency for Each Category
The relative frequency is calculated by dividing the frequency of each category by the total number of students surveyed.
- For 1 course:
[tex]\[
\text{Relative Frequency} = \frac{19}{50} = 0.38
\][/tex]
- For 2 courses:
[tex]\[
\text{Relative Frequency} = \frac{11}{50} = 0.22
\][/tex]
- For 3 courses:
Since there are 50 students in total and the frequencies for 1 and 2 courses sum up to 30 (19 + 11), the remaining frequency is for students taking 3 courses:
[tex]\[
\text{Frequency for 3 courses} = 50 - 30 = 20
\][/tex]
[tex]\[
\text{Relative Frequency} = \frac{20}{50} = 0.40
\][/tex]
#### Step 2: Calculate the Cumulative Frequency for Each Category
The cumulative frequency is the sum of frequencies for that category and all previous categories.
- For 1 course:
[tex]\[
\text{Cumulative Frequency} = 19
\][/tex]
- For 2 courses:
[tex]\[
\text{Cumulative Frequency} = 19 + 11 = 30
\][/tex]
- For 3 courses:
[tex]\[
\text{Cumulative Frequency} = 19 + 11 + 20 = 50
\][/tex]
So, the completed table is:
[tex]\[
\begin{array}{|l|l|l|l|}
\hline
\# \text{ of Courses} & \text{Frequency} & \text{Relative Frequency} & \text{Cumulative Frequency} \\
\hline
1 & 19 & 0.38 & 19 \\
\hline
2 & 11 & 0.22 & 30 \\
\hline
3 & 20 & 0.40 & 50 \\
\hline
\end{array}
\][/tex]
### Part (b): Percentage of Students Taking Exactly One Course
To find the percentage of students taking exactly one course, we take the frequency of students taking one course and divide it by the total number of students, then multiply by 100.
[tex]\[
\text{Percent of students taking exactly one course} = \left( \frac{19}{50} \right) \times 100 = 38.0\%
\][/tex]
So, the percentage of students taking exactly one course is [tex]\( \boxed{38.0 \%} \)[/tex].
