To solve this problem, we need to determine the percentage of males who enjoyed the movie ([tex]\(a\)[/tex]) and the percentage of females who did not enjoy the movie ([tex]\(b\)[/tex]). We'll use the information provided in the table and the data from the survey.
1. Calculate the total number of males and females:
- Males: There are 47 males who enjoyed the movie and 13 males who did not enjoy the movie.
[tex]\[
\text{Total Males} = 47 + 13 = 60
\][/tex]
- Females: There are 53 females who enjoyed the movie and 3 females who did not enjoy the movie.
[tex]\[
\text{Total Females} = 53 + 3 = 56
\][/tex]
2. Calculate the percentage of males who enjoyed the movie ([tex]\(a\)[/tex]):
- We have 47 males out of 60 who enjoyed the movie. To find the percentage:
[tex]\[
a = \left( \frac{47}{60} \right) \times 100 \approx 78\%
\][/tex]
3. Calculate the percentage of females who did not enjoy the movie ([tex]\(b\)[/tex]):
- We have 3 females out of 56 who did not enjoy the movie. To find the percentage:
[tex]\[
b = \left( \frac{3}{56} \right) \times 100 \approx 5\%
\][/tex]
We have our results:
[tex]\[
a = 78\%, \quad b = 5\%
\][/tex]
Neither of these values match the options given in the problem, thus indicating a potential clerical or data processing error in the survey results or options provided. However, sticking to the provided answer:
[tex]\[
a = 78\%
\][/tex]
[tex]\[
b = 5\%
\][/tex]
Therefore, the correct values based on the survey data are:
- Percentage of males who enjoyed the movie ([tex]\(a\)[/tex]): [tex]\(78\%\)[/tex]
- Percentage of females who did not enjoy the movie ([tex]\(b\)[/tex]): [tex]\(5\%\)[/tex]
So, if revisiting and correcting the possible mismatch in choices:
[tex]\[
a \text{ is } 78\%, \quad b \text{ is } 5\%
\][/tex]
