College

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

[tex]\[
\begin{array}{|l|l|l|l|l|l|}
\hline
\text{Viewer's Age Group} & \text{Excellent} & \text{Good} & \text{Average} & \text{Poor} & \text{Marginal Total} \\
\hline
16-25 & 52 & 42 & 12 & 7 & 113 \\
\hline
26-35 & 33 & 50 & 5 & 9 & 97 \\
\hline
36-45 & 58 & 12 & 28 & 34 & 132 \\
\hline
46-55 & 25 & 17 & 22 & 12 & 76 \\
\hline
56+ & 12 & 5 & 3 & 8 & 28 \\
\hline
\text{Marginal Total} & 180 & 126 & 70 & 70 & 446 \\
\hline
\end{array}
\][/tex]

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 46-55 age group who rated the film excellent is [tex]$\square$[/tex]%. Write your answer up to two decimal places.

Answer :

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

1. Identify the Total Number of Respondents from the 46-55 Age Group:
- From the table, you can see that there are 76 respondents in the 46-55 age group.

2. Identify the Number of Respondents Who Rated the Film "Excellent":
- In the 46-55 age group, 25 people rated the film as "excellent."

3. Calculate the Percentage:
- To find the percentage of the 46-55 age group that rated the film "excellent," use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of "Excellent" ratings}}{\text{Total number of respondents in age group}}\right) \times 100
\][/tex]
- Substituting the values we have:
[tex]\[
\text{Percentage} = \left(\frac{25}{76}\right) \times 100
\][/tex]

4. Calculate the Final Result:
- Perform the division and then multiply by 100 to get the percentage:
[tex]\[
\frac{25}{76} \approx 0.328947368
\][/tex]
- Multiplying by 100 gives approximately 32.89.

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