To find the relative frequency that people who prefer island vacations also prefer swimming, we need to look at the number of people who prefer swimming and the total number of people who prefer island vacations.
From the table, we can see:
- The number of people who prefer swimming at the island is 40.
- The total number of people who prefer island vacations combines those who prefer swimming and those who prefer hiking, which is \(40 + 12 = 52\).
Now, we can calculate the relative frequency of people who prefer swimming among those who prefer island vacations:
\[ \text{Relative Frequency} = \frac{\text{Number of people who prefer swimming}}{\text{Total number of people who prefer island vacations}} = \frac{40}{52} \]
Now, we can calculate this fraction:
\[ \frac{40}{52} \approx 0.7692 \]
To express this as a percentage, we multiply by 100:
\[ 0.7692 \times 100 \approx 76.92% \]
Rounding to the nearest tenth of a percent, we get:
\[ \text{Relative frequency} \approx 76.9% \]
Thus, the relative frequency that people who prefer island vacations also prefer swimming is 76.9%.