High School

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

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

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 46-55 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'll follow these steps:

1. Determine the Number of "Excellent" Responses:
- From the table, we see that 25 respondents from the 46-55 age group rated the film as excellent.

2. Find the Total Number of Respondents in the 46-55 Age Group:
- According to the table, the total number of respondents in this age group is 76.

3. Calculate the Percentage:
- We'll divide the number of "Excellent" ratings by the total number of respondents in the 46-55 age group and then multiply by 100 to get the percentage.
[tex]\[
\text{Percentage} = \left(\frac{25}{76}\right) \times 100
\][/tex]

4. Result:
- Performing the calculation, the percentage of respondents from the 46-55 age group who rated the film as excellent is approximately 32.89%.

Therefore, the percentage is approximately 32.89%.