To find the values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] in the relative frequency table for the survey results, follow these steps:
1. Calculate the total number of males and females surveyed:
- Males who enjoyed the movie: 47
- Males who did not enjoy the movie: 13
- Total males = 47 + 13 = 60
- Females who enjoyed the movie: 53
- Females who did not enjoy the movie: 3
- Total females = 53 + 3 = 56
2. Calculate the relative frequency of males who enjoyed the movie:
- We need to find what percentage of the total males surveyed enjoyed the movie.
- Relative frequency of males who enjoyed the movie = (Number of males who enjoyed / Total males) 100
- Relative frequency = (47 / 60) 100 ≈ 78
So, [tex]\( a \)[/tex] is 78%.
3. Calculate the relative frequency of females who did not enjoy the movie:
- We need to find what percentage of the total females surveyed did not enjoy the movie.
- Relative frequency of females who did not enjoy the movie = (Number of females who did not enjoy / Total females) 100
- Relative frequency = (3 / 56) 100 ≈ 5
So, [tex]\( b \)[/tex] is 5%.
Thus, the values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
[tex]\[ a = 78\%, \quad b = 5\% \][/tex]
These values do not match any given option in the provided choices, meaning there might be an error in the options given in the problem statement. However, based on the given calculations, the correct values are indeed [tex]\( a = 78\% \)[/tex] and [tex]\( b = 5\% \)[/tex].
