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.
| Viewer's Age Group | Excellent | Good | Average | Poor |
| :----------------- | :-------- | :--- | :------ | :--- |
| 16-25 | 52 | 42 | 12 | 7 |
| 26-35 | 33 | 50 | 5 | 9 |
| 36-45 | 58 | 12 | 28 | 34 |
| 46-55 | 25 | 17 | 22 | 12 |
| 56+ | 12 | 5 | 3 | 8 |
Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.
Out of the total respondents, the percentage of respondents from the [tex]$46-55$[/tex] age group who rated the film excellent is $\square$ %. Write your answer up to two decimal places.
Answer (2)
Divide the number of respondents from the 46-55 age group who rated the film excellent by the total number of respondents: 446 25 .
Multiply the result by 100 to express it as a percentage: 446 25 × 100 .
Calculate the percentage: 446 25 × 100 ≈ 5.605 .
Round the percentage to two decimal places: 5.61 .
Explanation
Understand the problem and provided data We are asked to find the percentage of respondents from the 46-55 age group who rated the film excellent, out of the total number of respondents. From the table, we can see that 25 respondents from the 46-55 age group rated the film excellent, and the total number of respondents is 446.
Plan the solution To find the percentage, we need to divide the number of respondents from the 46-55 age group who rated the film excellent by the total number of respondents, and then multiply by 100.
Set up the formula The percentage is calculated as follows: Total number of respondents Number of respondents from 46-55 age group who rated the film excellent × 100 Substituting the values from the table, we get: 446 25 × 100
Calculate the percentage Now, we perform the calculation: 446 25 × 100 ≈ 5.60538... Rounding the result to two decimal places, we get 5.61.
State the final answer Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is approximately 5.61%.
Examples
Understanding viewer preferences through surveys helps movie producers tailor their films to specific demographics. For example, if a producer finds that a certain age group particularly enjoys a specific genre, they might focus on creating more content in that genre. This data-driven approach ensures that the movie appeals to its target audience, increasing its chances of success. By analyzing the percentage of positive reviews from different age groups, producers can refine their marketing strategies and make informed decisions about future projects.
To find the percentage of respondents aged 46-55 who rated the film excellent, divide the 25 excellent ratings by the total of 446 respondents, resulting in approximately 5.61%.
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