To determine the percentage of respondents from the 46-55 age group who rated the film as excellent, follow these steps:
1. Identify the number of respondents in the 46-55 age group who rated the film as excellent. From the table, this number is [tex]\( 25 \)[/tex].
2. Determine the total number of respondents across all age groups. This total is given at the bottom right corner of the table as [tex]\( 446 \)[/tex].
3. Calculate the percentage by dividing the number of respondents from the 46-55 age group who rated the film excellent by the total number of respondents, and then multiplying by [tex]\( 100 \)[/tex].
The formula for calculating the percentage is:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of Excellent Ratings in 46-55 Age Group}}{\text{Total Number of Respondents}} \right) \times 100
\][/tex]
Substitute the given values into the formula:
[tex]\[
\text{Percentage} = \left( \frac{25}{446} \right) \times 100
\][/tex]
4. Express the final percentage up to two decimal places:
The percentage of respondents from the 46-55 age group who rated the film excellent is [tex]\( 5.61\)[/tex].
Therefore, the correct answer is [tex]\( 5.61 \)[/tex].
