To determine the percentage of respondents aged 46-55 who rated the film excellent, we need to follow these steps:
1. Identify the number of respondents aged 46-55 who rated the film excellent: According to the table, this number is 25.
2. Identify the total number of respondents aged 46-55: The table shows this as 76.
3. Calculate the percentage of respondents aged 46-55 who rated the film excellent:
- Use the formula for percentage:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of "Excellent" ratings}}{\text{Total respondents in age group}} \right) \times 100
\][/tex]
- Substitute the identified numbers:
[tex]\[
\text{Percentage} = \left( \frac{25}{76} \right) \times 100
\][/tex]
4. Compute the percentage value:
- Performing the division:
[tex]\[
\frac{25}{76} \approx 0.3289473684210527
\][/tex]
- Then multiply by 100 to get the percentage:
[tex]\[
0.3289473684210527 \times 100 \approx 32.89473684210527
\][/tex]
5. Round the result to two decimal places:
- The result rounded to two decimal places is:
[tex]\[
32.89
\][/tex]
Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is [tex]\(\boxed{32.89}\)[/tex]%.
