The table shows people's preferences for vacation activities (such swimming or hiking) and where they would want to go. Preferences Mountains Seaside Island Hiking 45 20 12 Swimming 12 53 40 Given the data in the table, what is the relative frequency that people who prefer island vacations also prefer swimming? Round the percentage to the nearest tenth.

1 answer

To find the relative frequency of people who prefer swimming among those who prefer island vacations, we need to first determine the total number of people who prefer island vacations and the number of those who prefer swimming.

From the table:

  • Preferences for the Island:
    • Hiking: 12
    • Swimming: 40

Now, we can calculate the total number of people who prefer vacations at the Island:

\[ \text{Total for Island} = \text{Hiking} + \text{Swimming} = 12 + 40 = 52 \]

Next, we need to find the number of people who prefer swimming at the Island:

  • Number of people who prefer swimming at the Island = 40

Now, we can calculate the relative frequency of people who prefer swimming given that they prefer the Island:

\[ \text{Relative Frequency} = \frac{\text{Number who prefer swimming at Island}}{\text{Total at Island}} = \frac{40}{52} \]

Now, let's calculate this fraction:

\[ \frac{40}{52} \approx 0.7692 \quad \text{(when calculated)} \]

To express this as a percentage, we multiply by 100:

\[ 0.7692 \times 100 \approx 76.92 \]

Rounding to the nearest tenth, we get:

\[ \approx 76.9% \]

Therefore, the relative frequency that people who prefer island vacations also prefer swimming is 76.9%.