Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

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

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 excellent, good, average, and poor.

Out of the total respondents, the percentage of respondents from the [tex]$46-55$[/tex] age group who rated the film excellent is [tex]$\square$[/tex]%. Write your answer up to two decimal places.

Answer :

To find the percentage of respondents from the 46-55 age group who rated the film as excellent, we follow these steps:

1. Identify the Total Number of Respondents in the 46-55 Age Group:
- According to the table, there are 76 respondents in the 46-55 age group.

2. Identify the Number of Respondents in the 46-55 Age Group Who Rated the Film Excellent:
- The table shows that 25 people in the 46-55 age group rated the film excellent.

3. Calculate the Percentage:
- To find the percentage of respondents who rated the film excellent, divide the number of excellent ratings by the total number of respondents in that age group, then multiply by 100 to convert it to a percentage.

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

4. Calculate and Round the Answer:
- When you perform the calculation, you get approximately 32.89.

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