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A movie producer held a preview screening of her new movie to find out how the film would be received by viewers of different age groups. The table shows the number of viewers of different age groups who rated the movie as excellent, average, or poor. Note: A rating of "excellent" means the audience liked the movie, while a rating of "poor" means the audience disliked the movie.

\begin{tabular}{|c|c|c|c|c|}
\hline Age Groups & Excellent & Average & Poor & \begin{tabular}{c}
Marginal \\
Total
\end{tabular} \\
\hline [tex]$16-30$[/tex] & 78 & 33 & 43 & 154 \\
\hline [tex]$30-44$[/tex] & 33 & 41 & 37 & 111 \\
\hline [tex]$45+$[/tex] & 38 & 23 & 20 & 81 \\
\hline \begin{tabular}{c}
Marginal \\
Total
\end{tabular} & 149 & 97 & 100 & 346 \\
\hline
\end{tabular}

Out of the total number of respondents, the percentage of respondents in the [tex]$30-44$[/tex] age group who rated the film as excellent, rounded to the nearest hundredth of a percent, is [tex]$\square \%$[/tex].



Answer :

GinnyAnswer
To solve the problem of finding the percentage of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent, we can follow these steps:

1. Identify the total number of respondents in the [tex]\(30-44\)[/tex] age group: From the table, we see that the total number of respondents in the [tex]\(30-44\)[/tex] age group is [tex]\(111\)[/tex].

2. Identify the number of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent: According to the table, this number is [tex]\(33\)[/tex].

3. Calculate the percentage of respondents who rated the film as excellent:
- Formula: [tex]\(\text{Percentage} = \left(\frac{\text{Number of excellent ratings}}{\text{Total number of respondents}} \right) \times 100\)[/tex]
- Plugging in the numbers: [tex]\[ \text{Percentage} = \left(\frac{33}{111} \right) \times 100 \][/tex]

4. Perform the division and multiplication:
- Calculate the division: [tex]\(\frac{33}{111} \approx 0.2973\)[/tex]
- Multiply by 100: [tex]\(0.2973 \times 100 \approx 29.73\)[/tex]

5. Round the result to the nearest hundredth of a percent: The percentage rounded to the nearest hundredth is [tex]\(29.73\%\)[/tex].

Thus, the percentage of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent, rounded to the nearest hundredth of a percent, is [tex]\(29.73\%\)[/tex].