High School

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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 & 9 & 97 \\

\hline

26-35 & 33 & 50 & 5 & & 88 \\

\hline

36-45 & 58 & 12 & 28 & 34 & 132 \\

\hline

46-55 & 25 & 17 & 22 & 12 & 76 \\

\hline

56+ & 12 & 5 & 3 & 70 & 90 \\

\hline

\text{Marginal Total} & 180 & 126 & 70 & 125 & 501 \\

\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 :

We are given that in the 46–55 age group, 25 respondents rated the film as excellent and there are 28 respondents in total. The percentage of respondents who rated the film excellent is calculated by dividing the number of excellent responses by the total number of responses in that age group and then multiplying the result by 100. That is,

[tex]$$
\text{Percentage} = \left(\frac{25}{28}\right) \times 100
$$[/tex]

Calculating the fraction:

[tex]$$
\frac{25}{28} \approx 0.892857
$$[/tex]

Multiplying by 100:

[tex]$$
0.892857 \times 100 \approx 89.2857
$$[/tex]

Rounded to two decimal places, the percentage is:

[tex]$$
89.29\%
$$[/tex]

Thus, the final answer is [tex]$89.29$[/tex].

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