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

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

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 (up to two decimal places): [tex]$\square$[/tex] \%.



Answer :

GinnyAnswer
To find the percentage of respondents from the [tex]$46-55$[/tex] age group who rated the film excellent, we follow these steps:

1. Identify the number of respondents from the [tex]$46-55$[/tex] age group who rated the film as excellent.
2. Identify the total number of respondents from the [tex]$46-55$[/tex] age group.
3. Calculate the percentage of respondents who rated the film excellent within this age group.
4. Round the result to two decimal places.

From the table:
- The number of respondents in the [tex]$46-55$[/tex] age group who rated the film excellent: 25
- The total number of respondents in the [tex]$46-55$[/tex] age group: 76

Now, calculate the percentage of respondents from the [tex]$46-55$[/tex] age group who rated the film excellent:
[tex]\[ \text{Percentage} = \left( \frac{\text{Number of Excellent Ratings}}{\text{Total Number of Respondents in Age Group}} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage} = \left( \frac{25}{76} \right) \times 100 \][/tex]

Given the detailed solution already, we know the result is:
[tex]\[ 32.89\% \][/tex]

So, the percentage of respondents from the [tex]$46-55$[/tex] age group who rated the film excellent is:

32.89 %.

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