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

\multicolumn{6}{|c|}{\text{Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.}} \\

\hline

\end{array}

\][/tex]

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]$\quad$[/tex] \%. Write your answer up to two decimal places.

Answer :

To find the percentage of respondents aged 46–55 who rated the film excellent, follow these steps:

1. Identify the number of respondents aged 46–55 who rated the film excellent. From the table, this number is
[tex]$$\text{Excellent} = 25.$$[/tex]

2. Identify the total number of respondents in the 46–55 age group. From the table, this total is
[tex]$$\text{Total} = 76.$$[/tex]

3. Calculate the percentage by dividing the number of excellent ratings by the total number of responses in that age group and then multiplying by 100:
[tex]$$\text{Percentage} = \left(\frac{25}{76}\right) \times 100.$$[/tex]

4. Performing the division and multiplication gives:
[tex]$$\text{Percentage} \approx 32.89\%.$$[/tex]

Thus, the percentage of respondents from the 46–55 age group who rated the film excellent is
[tex]$$32.89\%.$$[/tex]