Question

what is the relative frequency that the people who prefer island vacations also prefer swimming? round the percentage to the nearest 10th

Presences Mountains Seaside Island
hiking: 45 20 12
swimming: 12 53 40

Answer 1

To find the relative frequency of people who prefer island vacations and also prefer swimming, we first need to look at the data provided.

From the data:
- People who prefer island vacations and prefer swimming: 40
- Total number of people who prefer island vacations: \(12 + 40 = 52\) (12 who prefer hiking and 40 who prefer swimming)

Now we can calculate the relative frequency as follows:

\[
\text{Relative Frequency} = \frac{\text{Number of people who prefer swimming and island vacations}}{\text{Total number of people who prefer island vacations}} = \frac{40}{52}
\]

Calculating the fraction:

\[
\frac{40}{52} \approx 0.769230769230769
\]

To express this as a percentage:

\[
0.769230769230769 \times 100 \approx 76.9230769230769\%
\]

Now rounding to the nearest tenth:

\[
76.9\%
\]

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