Question

The distribution of hiking and swimming inclinations across mountain, seashore, and island locales is displayed in the table. Preferences Mountains Seaside Island Hiking 45 20 12 Swimming 12 53 40 Given the data in the table, what is the relative frequency that the people who prefer hiking also prefer mountains? Round the percentage to the nearest tenth.

Answer 1

To find the relative frequency that people who prefer hiking also prefer mountains, we need to follow these steps:

1. Calculate the total number of people who prefer hiking.

   From the table:

   • Hiking in Mountains: 45
   • Hiking at Seaside: 20
   • Hiking on Island: 12

   Total who prefer hiking = 45 + 20 + 12 = 77.

2. Identify the number of people who prefer hiking and also prefer mountains.

   From the table:

   • Hiking in Mountains: 45.

3. Calculate the relative frequency:

   The formula for relative frequency is: \[ \text{Relative Frequency} = \frac{\text{Number who prefer hiking and mountains}}{\text{Total number who prefer hiking}}. \]

   Substituting in our values: \[ \text{Relative Frequency} = \frac{45}{77} \approx 0.5844. \]

4. Convert it to a percentage: \[ 0.5844 \times 100 \approx 58.44. \]

5. Round to the nearest tenth: Rounding 58.44 to the nearest tenth gives us 58.4%.

Thus, the relative frequency that people who prefer hiking also prefer mountains is 58.4%.