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\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.

Sagot :

GinnyAnswer
To find 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.
2. Determine the total number of respondents in the 46-55 age group.
3. Use the formula for percentage: [tex]\[ \text{Percentage} = \left( \frac{\text{Number of excellent ratings}}{\text{Total number of ratings}} \right) \times 100 \][/tex]
4. Insert the identified values and calculate the percentage.
5. Round the answer to two decimal places.

Given:
- Number of respondents in the 46-55 age group who rated the film excellent: 25
- Total number of respondents in the 46-55 age group: 76

Using the formula:
[tex]\[ \text{Percentage} = \left( \frac{25}{76} \right) \times 100 \approx 32.89 \][/tex]

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