There are 628 students in Tan’s high school. Tan surveys 120 randomly chosen students about their favorite movie genre. The results are as follows.
Movie genre Number of students/Frequency
Science Fiction 24
Horror 11
Comedy 27
Action 10
Animated 48
Based on Tan’s sample data, approximately how many students in the school prefer animated movies?
(1 point)
To find the approximate number of students in the school who prefer animated movies, we need to use the concept of sampling.
According to the survey data, out of 120 randomly chosen students, 48 preferred animated movies.
We can set up a proportion using this information:
(Number of students who prefer animated movies in the sample) / (Total number of students in the sample) = (Number of students who prefer animated movies in the population) / (Total number of students in the population)
Using the given information, we have:
48 / 120 = x / 628
Now, we can solve for "x", the approximate number of students in the school who prefer animated movies.
Cross multiplying the proportion, we get:
(48 * 628) = (120 * x)
Simplifying, we have:
30144 = 120x
To isolate "x", divide both sides by 120:
x ≈ 30144 / 120 ≈ 251.2
Therefore, approximately 251 students in the school prefer animated movies.
Approximately 76 students (12% of the total students in the school) prefer animated movies based on the sample data.
To find this, you can use the formula:
proportion of students who prefer animated movies = frequency of students who prefer animated movies / total number of students in the sample
proportion = 48 / 120 = 0.4
Then, you can estimate the number of students in the school who prefer animated movies by multiplying the proportion by the total number of students:
estimated number of students who prefer animated movies = proportion * total number of students
estimated number = 0.4 * 628 = 251.2
Rounding to the nearest whole number gives an estimate of 76 students who prefer animated movies.