Answer :
To solve the problem of finding the percentage of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent, we can follow these steps:
1. Identify the total number of respondents in the [tex]\(30-44\)[/tex] age group: From the table, we see that the total number of respondents in the [tex]\(30-44\)[/tex] age group is [tex]\(111\)[/tex].
2. Identify the number of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent: According to the table, this number is [tex]\(33\)[/tex].
3. Calculate the percentage of respondents who rated the film as excellent:
- Formula: [tex]\(\text{Percentage} = \left(\frac{\text{Number of excellent ratings}}{\text{Total number of respondents}} \right) \times 100\)[/tex]
- Plugging in the numbers: [tex]\[ \text{Percentage} = \left(\frac{33}{111} \right) \times 100 \][/tex]
4. Perform the division and multiplication:
- Calculate the division: [tex]\(\frac{33}{111} \approx 0.2973\)[/tex]
- Multiply by 100: [tex]\(0.2973 \times 100 \approx 29.73\)[/tex]
5. Round the result to the nearest hundredth of a percent: The percentage rounded to the nearest hundredth is [tex]\(29.73\%\)[/tex].
Thus, the percentage of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent, rounded to the nearest hundredth of a percent, is [tex]\(29.73\%\)[/tex].
1. Identify the total number of respondents in the [tex]\(30-44\)[/tex] age group: From the table, we see that the total number of respondents in the [tex]\(30-44\)[/tex] age group is [tex]\(111\)[/tex].
2. Identify the number of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent: According to the table, this number is [tex]\(33\)[/tex].
3. Calculate the percentage of respondents who rated the film as excellent:
- Formula: [tex]\(\text{Percentage} = \left(\frac{\text{Number of excellent ratings}}{\text{Total number of respondents}} \right) \times 100\)[/tex]
- Plugging in the numbers: [tex]\[ \text{Percentage} = \left(\frac{33}{111} \right) \times 100 \][/tex]
4. Perform the division and multiplication:
- Calculate the division: [tex]\(\frac{33}{111} \approx 0.2973\)[/tex]
- Multiply by 100: [tex]\(0.2973 \times 100 \approx 29.73\)[/tex]
5. Round the result to the nearest hundredth of a percent: The percentage rounded to the nearest hundredth is [tex]\(29.73\%\)[/tex].
Thus, the percentage of respondents in the [tex]\(30-44\)[/tex] age group who rated the film as excellent, rounded to the nearest hundredth of a percent, is [tex]\(29.73\%\)[/tex].