A movie producer conducted a survey after a preview screening of her new movie to find out how the film would be received by viewers from different age groups. The table shows the numbers of viewers in different age groups who rated the film as excellent, good, average, or poor.

[tex]\[
\begin{array}{|l|r|r|r|r|r|}
\hline
\text{Viewer's Age Group} & \text{Excellent} & \text{Good} & \text{Average} & \text{Poor} & \text{Marginal Total} \\
\hline
16-25 & 52 & 42 & 12 & 7 & 113 \\
\hline
26-35 & 33 & 50 & 5 & 9 & 97 \\
\hline
36-45 & 58 & 12 & 28 & 34 & 132 \\
\hline
46-55 & 25 & 17 & 22 & 12 & 76 \\
\hline
56+ & 12 & 5 & 3 & 8 & 28 \\
\hline
\text{Marginal Total} & 180 & 126 & 70 & 70 & 446 \\
\hline
\end{array}
\][/tex]

Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.

Calculate the percentage of respondents from the 46-55 age group who rated the film excellent, rounded to two decimal places.

[tex]$\square$[/tex] %

Write your answer.

To find out the percentage of respondents from the 46-55 age group who rated the film as "excellent," you need to follow these steps:

1. Identify the Number of Respondents from the 46-55 Age Group Who Rated the Film Excellent:
- According to the table, 25 people from the 46-55 age group rated the film as "excellent."

2. Find the Total Number of Respondents in the 46-55 Age Group:
- The total number of respondents from the 46-55 age group is 76.

3. Calculate the Percentage:
- To find the percentage of respondents in the 46-55 age group who rated the film excellent, use the formula for percentage:

[tex]\[
\text{Percentage} = \left(\frac{\text{Number of Excellent Ratings}}{\text{Total Number of Respondents in Age Group}}\right) \times 100
\][/tex]

- Plug in the numbers:

[tex]\[
\text{Percentage} = \left(\frac{25}{76}\right) \times 100
\][/tex]

4. Calculate and Round Your Answer:
- Calculate the division first and then multiply by 100 to get the percentage.

[tex]\[
\text{Percentage} \approx 32.89\%
\][/tex]

Therefore, the percentage of respondents from the 46-55 age group who rated the film as "excellent" is 32.89%.