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\begin{tabular}{|l|r|r|r|r|r|}
\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}

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 [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 aged 46-55 who rated the film excellent, we need to follow these steps:

1. Identify the number of respondents aged 46-55 who rated the film excellent: According to the table, this number is 25.

2. Identify the total number of respondents aged 46-55: The table shows this as 76.

3. Calculate the percentage of respondents aged 46-55 who rated the film excellent:
- Use the formula for percentage:
[tex]\[ \text{Percentage} = \left( \frac{\text{Number of "Excellent" ratings}}{\text{Total respondents in age group}} \right) \times 100 \][/tex]
- Substitute the identified numbers:
[tex]\[ \text{Percentage} = \left( \frac{25}{76} \right) \times 100 \][/tex]

4. Compute the percentage value:
- Performing the division:
[tex]\[ \frac{25}{76} \approx 0.3289473684210527 \][/tex]
- Then multiply by 100 to get the percentage:
[tex]\[ 0.3289473684210527 \times 100 \approx 32.89473684210527 \][/tex]

5. Round the result to two decimal places:
- The result rounded to two decimal places is:
[tex]\[ 32.89 \][/tex]

Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is [tex]\(\boxed{32.89}\)[/tex]%.

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