College

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

[tex]
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Viewer's Age Group} & \text{Excellent} & \text{Good} & \text{Average} & \text{Poor} & \text{Marginal Total} \\
\hline
16-25 & & & & & \\
\hline
26-35 & 52 & 42 & 12 & 7 & 113 \\
\hline
36-45 & 33 & 50 & 5 & 9 & 97 \\
\hline
46-55 & 58 & 12 & 28 & 34 & 132 \\
\hline
56+ & 2 & 17 & 22 & 12 & 76 \\
\hline
\text{Marginal Total} & 145 & 121 & 67 & 62 & 395 \\
\hline
\end{array}
\]
[/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 [tex]$46-55$[/tex] age group who rated the film excellent is [tex]\(\square\%\)[/tex]. Write your answer up to two decimal places.

Answer :

To determine the percentage of respondents from the 46-55 age group who rated the film as excellent, we need to follow these steps:

1. Identify the Number of Excellent Ratings in the 46-55 Age Group:
From the table, there are 58 people in the 46-55 age group who rated the film as excellent.

2. Identify the Total Number of Respondents in the 46-55 Age Group:
The total number of respondents in the 46-55 age group is 132.

3. Calculate the Percentage:
- The percentage is found by dividing the number of excellent ratings by the total number of respondents in the 46-55 age group, then multiplying by 100 to convert it to a percentage:

[tex]\[ \text{Percentage} = \left( \frac{58}{132} \right) \times 100 \][/tex]

4. Result:
- Performing this calculation gives us approximately 43.94%.

Therefore, about 43.94% of the respondents from the 46-55 age group rated the film as excellent.