To find the relative frequency of people who prefer swimming out of those who prefer island vacations, we'll first gather the relevant data from the table.
From the table:
- The number of people who prefer hiking and would go to the Island is 12.
- The number of people who prefer swimming and would go to the Island is 40.
Now we can calculate the total number of people who prefer island vacations by adding those who prefer hiking and those who prefer swimming:
\[ \text{Total Island Preferences} = \text{Hiking (Island)} + \text{Swimming (Island)} = 12 + 40 = 52 \]
Now we can find the number of island vacationers who prefer swimming, which is 40.
Next, we'll calculate the relative frequency of people who prefer swimming out of those who prefer island vacations:
\[ \text{Relative Frequency (Swimming)} = \frac{\text{Number who prefer Swimming (Island)}}{\text{Total Island Preferences}} = \frac{40}{52} \]
Now we will convert this fraction into a percentage:
\[ \frac{40}{52} \approx 0.7692 \]
Multiplying by 100 to convert to a percentage:
\[ 0.7692 \times 100 \approx 76.92 \]
Now, rounding to the nearest tenth gives us:
\[ \approx 76.9% \]
Thus, the relative frequency that people who prefer island vacations also prefer swimming is 76.9%.