High School

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[tex]
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Viewer's Age Group} & \text{Excellent} & \text{Good} & \text{Average} & \text{Poor} & \text{Marginal Total} \\
\hline
16-25 & 52 & 42 & 12 & 7 & 113 \\
\hline
26-35 & 33 & 50 & 5 & 9 & 97 \\
\hline
36-45 & 58 & 12 & 28 & 34 & 132 \\
\hline
46-55 & 25 & 17 & 22 & 12 & 76 \\
\hline
56+ & 12 & 5 & 3 & 8 & 28 \\
\hline
\text{Marginal Total} & 180 & 126 & 70 & 70 & 446 \\
\hline
\multicolumn{6}{|l|}{\text{Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.}} \\
\hline
\end{array}
\]
[/tex]

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, what is the percentage of respondents from the 46-55 age group who rated the film excellent? (Round to two decimal places.)

[tex]\(\square\)[/tex] \%

Answer :

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

1. Identify the number of viewers from the 46-55 age group who rated the film as excellent.
- From the table, we see that 25 viewers in the 46-55 age group rated the film excellent.

2. Identify the total number of respondents from the 46-55 age group.
- The total number of respondents in this age group is 76, as shown in the table.

3. Calculate the percentage of respondents who rated the film excellent.
- To find this percentage, use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of Excellent ratings}}{\text{Total respondents in the age group}}\right) \times 100
\][/tex]

4. Plug the numbers into the formula:
- Substitute 25 for the number of excellent ratings and 76 for the total number of respondents in the age group:
[tex]\[
\text{Percentage} = \left(\frac{25}{76}\right) \times 100
\][/tex]

5. Calculate the result and round to two decimal places:
- After calculating the percentage, you get approximately 32.89%.

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

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