High School

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

[tex]\[

\begin{array}{|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 & \\

\hline

26-35 & 33 & 50 & 5 & 9 & \\

\hline

36-45 & 58 & 12 & 28 & 34 & 97 \\

\hline

46-55 & 25 & 17 & 22 & 12 & 76 \\

\hline

56+ & 12 & 5 & 3 & 8 & 28 \\

\hline

\text{Marginal Total} & 180 & 126 & 70 & 70 & \\

\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 :

Sure! Let's go through the steps to calculate the percentage of respondents from the 46-55 age group who rated the film as excellent:

1. Identify the Number of Excellent Ratings:
- From the age group 46-55, the number of people who rated the film excellent is 25.

2. Identify the Total Number of Respondents in the Age Group:
- The total number of respondents in the 46-55 age group is 76.

3. Calculate the Percentage:
- To find the percentage of respondents who rated the film excellent, you calculate:

[tex]\[
\text{Percentage} = \left(\frac{\text{Number of Excellent Ratings}}{\text{Total Respondents in the Age Group}}\right) \times 100
\][/tex]

- Plug in the numbers:

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

4. Round Your Answer:
- Calculate the result and round it to two decimal places:

[tex]\[
\text{Percentage} \approx 32.89\%
\][/tex]

Therefore, about 32.89% of respondents in the 46-55 age group rated the film as excellent.

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