Use the table to answer the question.

Question

Determining the proportion of eighth graders that favor cats based on their overall enrollment.
Preference 7th Graders 8th Graders
Prefers Cats 36 22
Prefers Dogs 8 26
No Preference 2 6
What is the relative frequency of 8th graders who prefer cats? Round the percentage to the nearest tenth.

(1 point)
Responses

37.9%
37.9%

40.7%
40.7%

78.2%
78.2%

22%

Answer 1

To find the relative frequency of 8th graders who prefer cats, we need to determine the total number of 8th graders surveyed and then find the proportion of them who prefer cats.

From the table:

• 8th graders who prefer cats: 22
• 8th graders who prefer dogs: 26
• 8th graders with no preference: 6

First, let's find the total number of 8th graders: \[ \text{Total 8th Graders} = \text{Prefers Cats} + \text{Prefers Dogs} + \text{No Preference} \] \[ \text{Total 8th Graders} = 22 + 26 + 6 = 54 \]

Now, we can calculate the relative frequency of 8th graders who prefer cats: \[ \text{Relative Frequency} = \frac{\text{Number of 8th Graders who prefer cats}}{\text{Total Number of 8th Graders}} \] \[ \text{Relative Frequency} = \frac{22}{54} \]

Now, calculating that: \[ \text{Relative Frequency} \approx 0.4074074074 \]

To express this as a percentage, we multiply by 100: \[ \text{Percentage} \approx 40.74074074% \]

Rounding to the nearest tenth, we get: \[ 40.7% \]

So the relative frequency of 8th graders who prefer cats is 40.7%.

The correct response is: 40.7%