A movie producer conducted a survey after the screening of a 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 determine 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 people in the 16-25 age group who gave a poor rating: According to the table, there are 7 people in this age group who rated the movie as "poor."

2. Find the total number of people in the 16-25 age group: The table shows that there are 113 viewers in this age group.

3. Calculate the percentage: To find the percentage of people in the 16-25 age group who gave a poor rating, use the formula:

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

Plugging in the numbers:

[tex]\[
\text{Percentage} = \left(\frac{7}{113}\right) \times 100
\][/tex]

4. Compute the result: Carrying out the division and multiplication gives approximately 6.19%.

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: 6.19%.