To solve this problem, we need to determine the relative frequency values for the survey data, and then match them to the closest percentage values given in the options.
Here’s the detailed step-by-step solution:
1. Calculate the total number of males surveyed:
- Males who enjoyed the movie: [tex]\(47\)[/tex]
- Males who did not enjoy the movie: [tex]\(13\)[/tex]
- Total males surveyed = [tex]\(47 + 13 = 60\)[/tex]
2. Calculate the relative frequency of males who enjoyed the movie:
- Relative frequency = (Number of males who enjoyed the movie / Total number of males surveyed) [tex]\(\times 100\)[/tex]
- Relative frequency = [tex]\((47 / 60) \times 100 \approx 78\)[/tex]% (rounded to the nearest percent)
- This gives [tex]\(a = 78\%\)[/tex]
3. Calculate the total number of females surveyed:
- Females who enjoyed the movie: [tex]\(53\)[/tex]
- Females who did not enjoy the movie: [tex]\(3\)[/tex]
- Total females surveyed = [tex]\(53 + 3 = 56\)[/tex]
4. Calculate the relative frequency of females who did not enjoy the movie:
- Relative frequency = (Number of females who did not enjoy the movie / Total number of females surveyed) [tex]\(\times 100\)[/tex]
- Relative frequency = [tex]\((3 / 56) \times 100 \approx 5\)[/tex]% (rounded to the nearest percent)
- This gives [tex]\(b = 5\%\)[/tex]
Looking at these values, it appears the confusion in the given options might be due to a mismatch. Given our calculations:
- [tex]\(a = 78\%\)[/tex]
- [tex]\(b = 5\%\)[/tex]
But unfortunately, none of the given options match our calculated values:
- [tex]\(a = 40\%, b = 4\%\)[/tex]
- [tex]\(a = 41\%, b = 3\%\)[/tex]
- [tex]\(a = 47\%, b = 3\%\)[/tex]
- [tex]\(a = 41\%, b = 19\%\)[/tex]
There appear to be no exact matches, likely due to discrepancies in the options provided or a misidentification of variates in the problem. Hence, the correct answer isn't among the provided choices:
[tex]\[
\boxed{There is an error in the options provided}
\][/tex]
