Answer :
To solve the problem of filling out the table with the correct percentages, let's break down the steps systematically:
1. Calculate Total Respondents:
- Males who enjoyed the movie: 47
- Males who did not enjoy the movie: 13
- Females who enjoyed the movie: 53
- Females who did not enjoy the movie: 3
Total males = 47 (enjoyed) + 13 (did not enjoy) = 60
Total females = 53 (enjoyed) + 3 (did not enjoy) = 56
Total respondents = 60 (males) + 56 (females) = 116
2. Calculate Percentages:
- Percentage of males who enjoyed the movie:
[tex]\[ \text{Males Enjoyed Percentage} = \left( \frac{47}{116} \right) \times 100 \approx 40.52\% \][/tex]
Rounded to the nearest percent: 41%
- Percentage of females who did not enjoy the movie:
[tex]\[ \text{Females Did Not Enjoy Percentage} = \left( \frac{3}{116} \right) \times 100 \approx 2.59\% \][/tex]
Rounded to the nearest percent: 3%
3. Fill the Table with Given Values:
- The percentage of males who did not enjoy the movie: Given as 11%
- The percentage of females who enjoyed the movie: Given as 46%
4. Verify the Values:
- The value for "Total" should sum up to 100%
So, the values for \(a\) and \(b\) are already calculated and rounded. Based on the options provided:
The correct answers are \(a = 41\%\) and \(b = 3\%\).
Thus, the correct choice is:
[tex]\(a = 41\%, b = 3\%\)[/tex]
1. Calculate Total Respondents:
- Males who enjoyed the movie: 47
- Males who did not enjoy the movie: 13
- Females who enjoyed the movie: 53
- Females who did not enjoy the movie: 3
Total males = 47 (enjoyed) + 13 (did not enjoy) = 60
Total females = 53 (enjoyed) + 3 (did not enjoy) = 56
Total respondents = 60 (males) + 56 (females) = 116
2. Calculate Percentages:
- Percentage of males who enjoyed the movie:
[tex]\[ \text{Males Enjoyed Percentage} = \left( \frac{47}{116} \right) \times 100 \approx 40.52\% \][/tex]
Rounded to the nearest percent: 41%
- Percentage of females who did not enjoy the movie:
[tex]\[ \text{Females Did Not Enjoy Percentage} = \left( \frac{3}{116} \right) \times 100 \approx 2.59\% \][/tex]
Rounded to the nearest percent: 3%
3. Fill the Table with Given Values:
- The percentage of males who did not enjoy the movie: Given as 11%
- The percentage of females who enjoyed the movie: Given as 46%
4. Verify the Values:
- The value for "Total" should sum up to 100%
So, the values for \(a\) and \(b\) are already calculated and rounded. Based on the options provided:
The correct answers are \(a = 41\%\) and \(b = 3\%\).
Thus, the correct choice is:
[tex]\(a = 41\%, b = 3\%\)[/tex]
