Question

as people exited a movie theater, they were informally surveyed about whether they enjoyed the movie or not.
males
enjoyed: 47
did not enjoy: 13
females
enjoyed: 53
did not enjoy: 3
survey on movie

	enjoyed	did not enjoy	total
females	46%	b

what are the values of a and b in the relative frequency table for the survey results? round answers to the nearest percent.

• $a = 40\\%$, $b = 4\\%$
• $a = 41\\%$, $b = 3\\%$
• $a = 47\\%$, $b = 3\\%$
• $a = 41\\%$, $b = 19\\%$

Explanation:

Step1: Calculate total number of males

Males who enjoyed: 47, did not enjoy: 13. Total males = 47 + 13 = 60.

Step2: Calculate relative frequency \(a\) (males who enjoyed)

\(a=\frac{47}{60}\times100\%\approx78.33\%\)? Wait, no, wait. Wait, the table has females' enjoyed as 46%. Wait, total people: males (47+13=60), females (53+3=56). Total surveyed: 60 + 56 = 116.
Wait, females who enjoyed: 53. So relative frequency for females enjoyed: \(\frac{53}{116}\times100\%\approx45.69\%\), which is rounded to 46% as given. So total is 116.
Now, males who enjoyed: 47. So \(a=\frac{47}{116}\times100\%\approx40.52\%\approx41\%\).

Step3: Calculate total females: 53 + 3 = 56. Relative frequency for females did not enjoy: \(b=\frac{3}{116}\times100\%\approx2.59\%\approx3\%\).

Answer:

B. \(a = 41\%, b = 3\%\)