Let's analyze the data provided and find the required percentages step-by-step.
### (a) What percentage of the students passed math?
To find the percentage of students who passed math, we need to determine how many students passed and then calculate the percentage of the total number of students.
- The number of students who passed math is given by:
[tex]\[
\text{Passed math} = 32 \, (\text{live on campus}) + 66 \, (\text{live off campus}) = 98
\][/tex]
- The total number of students is 200.
Therefore, the percentage of students who passed math is:
[tex]\[
\frac{98}{200} \times 100\% = 49\%
\][/tex]
### (b) What percentage of the students live off campus?
To find the percentage of students who live off campus, we need to determine the total number of students living off campus and then calculate the percentage of the total number of students.
- The number of students living off campus is given by:
[tex]\[
\text{Live off campus} = 66 \, (\text{passed}) + 22 \, (\text{failed}) = 88
\][/tex]
Therefore, the percentage of students who live off campus is:
[tex]\[
\frac{88}{200} \times 100\% = 44\%
\][/tex]
### (c) What percentage of the students who live off campus passed math?
To find this percentage, we need to calculate the number of students who live off campus and passed math, and then find what percentage this is of the total number of students living off campus.
- The number of students who live off campus and passed math is 66.
- The total number of students who live off campus is 88.
Therefore, the percentage of students who live off campus and passed math is:
[tex]\[
\frac{66}{88} \times 100\% = 75\%
\][/tex]
### (d) Is there evidence that students who live off campus tend to pass math more often than average?
To determine if students who live off campus pass math more often than the average student, we compare the percentage of off-campus students who passed (from part (c)) with the overall percentage of students who passed (from part (a)).
- Percentage of students who passed math overall (part (a)): [tex]\(49\%\)[/tex]
- Percentage of off-campus students who passed math (part (c)): [tex]\(75\%\)[/tex]
Considering these percentages, we can conclude:
[tex]\[
\text{Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).}
\][/tex]
Putting it all together:
[tex]\[
\begin{array}{l}
\text{(a) } 49\% \\
\text{(b) } 44\% \\
\text{(c) } 75\% \\
\text{(d) Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).}
\end{array}
\][/tex]
