Question

the table shows peoples preferences for vacation activities such wswimming 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

Answer 1

To find the relative frequency of people who prefer island vacations and also prefer swimming, we can use the following formula:

\[
\text{Relative Frequency} = \frac{\text{Number of people who prefer swimming on the island}}{\text{Total number of people who prefer island vacations}} \times 100
\]

From the table data:

- The number of people who prefer swimming on the island = 40
- The total number of people who prefer island vacations can be calculated by adding all preferences for the island:

\[
\text{Total for island} = \text{hiking} + \text{swimming} = 12 + 40 = 52
\]

Now, we can substitute these values into the relative frequency formula:

\[
\text{Relative Frequency} = \frac{40}{52} \times 100
\]

Calculating this gives:

\[
\text{Relative Frequency} \approx \frac{40}{52} \approx 0.7692 \times 100 \approx 76.92\%
\]

Rounding to the nearest tenth:

\[
\text{Relative Frequency} \approx 76.9\%
\]

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