Use the table to answer the question.

Swimming
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 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 first need to determine the total number of people who prefer island vacations and how many of those prefer swimming.

From the table:

  • People who prefer swimming at the island = 40
  • People who prefer hiking at the island = 12

Now, let's calculate the total number of people who prefer island vacations:

\[ \text{Total island preferences} = \text{Hiking at island} + \text{Swimming at island} = 12 + 40 = 52 \]

Next, we find the relative frequency of swimming preferences among those who prefer island vacations:

\[ \text{Relative frequency} = \frac{\text{Number of people who prefer swimming at island}}{\text{Total number of people who prefer island}} \]

Substituting the counted values:

\[ \text{Relative frequency} = \frac{40}{52} \]

Now, we can convert this into a percentage by multiplying by 100:

\[ \text{Percentage} = \left(\frac{40}{52}\right) \times 100 \]

Calculating that:

\[ \text{Percentage} = \left(\approx 0.7692\right) \times 100 \approx 76.9% \]

So, the relative frequency that people who prefer island vacations also prefer swimming, rounded to the nearest tenth, is 76.9%.