High School

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[tex]
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Viewer's Age Group} & \text{Excellent} & & \text{Good} & & \text{Average} & & \text{Poor} & & \text{Marginal Total} & \\
\hline
16-25 & & 52 & & 42 & & 12 & & 7 & & 113 \\
\hline
26-35 & & 33 & & 50 & & 5 & & 9 & & 97 \\
\hline
36-45 & & 58 & & 12 & & 28 & & 34 & & 132 \\
\hline
46-55 & & 25 & & 17 & & 22 & & 12 & & 76 \\
\hline
56+ & & 12 & & 5 & & 3 & & 8 & & 28 \\
\hline
\text{Marginal Total} & & 180 & & 126 & & 70 & & 70 & & 446 \\
\hline
\multicolumn{11}{|l|}{\text{Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.}} \\
\hline
\end{array}
\]

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.

Answer :

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

1. Identify the Relevant Numbers:
- From the table, find the number of people in the 46-55 age group who rated the film as "Excellent". This number is 25.
- Also, find the total number of respondents in the 46-55 age group, which is 76.

2. Calculate the Percentage:
- Use the formula for percentage:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of Excellent ratings in age group}}{\text{Total number of respondents in age group}} \right) \times 100
\][/tex]
- Substitute the identified values into the formula:
[tex]\[
\text{Percentage} = \left( \frac{25}{76} \right) \times 100
\][/tex]

3. Compute the Result:
- Solve the fraction and then multiply by 100 to convert it to a percentage.
- The result is approximately 32.89%.

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

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