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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 [tex]$\square$[/tex]%. Write your answer up to two decimal places.



Answer :

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

1. Identify the number of respondents in the 46-55 age group who rated the film as excellent. From the table, this number is [tex]\( 25 \)[/tex].

2. Determine the total number of respondents across all age groups. This total is given at the bottom right corner of the table as [tex]\( 446 \)[/tex].

3. Calculate the percentage by dividing the number of respondents from the 46-55 age group who rated the film excellent by the total number of respondents, and then multiplying by [tex]\( 100 \)[/tex].

The formula for calculating the percentage is:
[tex]\[ \text{Percentage} = \left( \frac{\text{Number of Excellent Ratings in 46-55 Age Group}}{\text{Total Number of Respondents}} \right) \times 100 \][/tex]

Substitute the given values into the formula:
[tex]\[ \text{Percentage} = \left( \frac{25}{446} \right) \times 100 \][/tex]

4. Express the final percentage up to two decimal places:

The percentage of respondents from the 46-55 age group who rated the film excellent is [tex]\( 5.61\)[/tex].

Therefore, the correct answer is [tex]\( 5.61 \)[/tex].

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