High School

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

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

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 :

- Calculate the percentage of respondents from the 46-55 age group who rated the film excellent.
- Use the formula: $\frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100$.
- Substitute the values: $\frac{25}{446} \times 100$.
- The percentage is approximately: $\boxed{5.61}\%$.

### Explanation
1. Understand the problem and provided data
We need to find the percentage of respondents from the 46-55 age group who rated the film excellent, out of the total respondents. From the table, we see that 25 respondents from the 46-55 age group rated the film excellent. The total number of respondents is 446.

2. State the formula
To find the percentage, we use the formula: $$ \text{Percentage} = \frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100 $$

3. Substitute the values
Substitute the values into the formula: $$ \text{Percentage} = \frac{25}{446} \times 100 $$

4. Calculate the result
Calculate the percentage: $$ \text{Percentage} = \frac{25}{446} \times 100 \approx 5.60538116591704 \approx 5.61 $$ Rounded to two decimal places, the percentage is 5.61%.

5. State the final answer
Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is approximately 5.61%.

### Examples
Understanding audience preferences through surveys is crucial in the movie industry. For example, a producer can use this percentage to gauge the film's appeal to a specific age group and tailor marketing strategies accordingly. If a particular age group shows a strong liking for the movie, the marketing team might focus on advertising channels popular among that demographic. This targeted approach can significantly improve the film's box office success.