A survey is conducted at a school where a random sample of 40 students is asked about their favourite club. The responses are: 14 students: Science Club | 11 students: Arts Club | 9 students: Sports Club | 6 students: Debate Club. Assume there are 800 students in the whole school.
What is the probability that a randomly chosen student from the sample prefers the Arts Club?
Number of students preferring Arts Club = 11
Total number of students in the sample = 40
Probability = (Number of favourable outcomes) / (Total possible outcomes)
P(Arts Club) = 11 / 40 = 0.275 or 27.5%
Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club.
Number of students preferring Sports Club in sample = 9
Total number of students in sample = 40
Probability of Sports Club = 9 / 40
Total number of students in school = 800
Estimated number of students = Probability × Total students in school
Estimated students = (9 / 40) × 800 = = 180 students.
Explanation
The solution applies the formula for statistical probability from the sample data: Probability = Favourable Outcomes / Total Outcomes. For the estimation, it uses the sample probability to predict the population preference, mirroring the textbook's example of estimating quantities for a whole school based on a class sample.