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A movie producer conducted a survey after the screening of his movie to find out how the film would be received by viewers from different age groups. The columns in the two-way table indicate the numbers of viewers who rated the film on a four-point scale: excellent, good, average, and poor.

[tex]\[

\begin{tabular}{|c|c|c|c|c|c|}

\hline

\begin{tabular}{c}

Viewer's \\

Age \\

Group

\end{tabular} & Excellent & Good & Average & Poor & \begin{tabular}{c}

Marginal \\

Totals

\end{tabular} \\

\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

\begin{tabular}{c}

56 and \\

Above

\end{tabular} & 12 & 5 & 3 & 8 & 28 \\

\hline

\begin{tabular}{c}

Marginal \\

Totals

\end{tabular} & 180 & 126 & 70 & 70 & 446 \\

\hline

\end{tabular}

\][/tex]

Select the correct answer.

What percentage of the audience from the 16-25 age group gave the movie a poor rating?

A. [tex]$6.19\%$[/tex]
B. [tex]$10.00\%$[/tex]
C. [tex]$25.34\%$[/tex]
D. [tex]$15.70\%$[/tex]
E. [tex]$16.22\%$[/tex]

Answer :

To find the percentage of the audience from the 16-25 age group who gave the movie a poor rating, follow these steps:

1. Identify the Number of Poor Ratings for the Age Group 16-25:
From the table, the number of viewers in the 16-25 age group giving a poor rating is 7.

2. Identify the Total Number of Viewers in the Age Group 16-25:
The total number of viewers from the 16-25 age group is 113.

3. Calculate the Percentage of Poor Ratings:
Use the formula for percentage:

[tex]\[
\text{Percentage of Poor Ratings} = \left(\frac{\text{Number of Poor Ratings}}{\text{Total Number of Viewers}}\right) \times 100
\][/tex]

Substituting the known values:

[tex]\[
\text{Percentage of Poor Ratings} = \left(\frac{7}{113}\right) \times 100 \approx 6.19\%
\][/tex]

Therefore, the percentage of the audience from the 16-25 age group who gave the movie a poor rating is approximately 6.19%. The correct answer is option A.

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