QUESTION 2
Easy
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.
(i) What is the probability that a randomly chosen student from the sample prefers the Arts Club?
(ii) Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club.
SOLUTION
1
Note down the given data
Total students surveyed \(= 40\)
Total students in the school \(= 800\)
| Club | Number of Students |
|---|---|
| Science Club | 14 |
| Arts Club | 11 |
| Sports Club | 9 |
| Debate Club | 6 |
Total students in the school \(= 800\)
2
(i) Find probability that a student prefers Arts Club
Number of students who prefer Arts Club \(= 11\)
Total students surveyed \(= 40\)
\(P(Arts\, Club) = \frac{11}{40}\) or \(0.275\)
The probability that a randomly chosen student prefers the Arts Club is \(\frac{11}{40}\).
Total students surveyed \(= 40\)
\(P(Arts\, Club) = \frac{11}{40}\) or \(0.275\)
The probability that a randomly chosen student prefers the Arts Club is \(\frac{11}{40}\).
3
Estimate how many students in the whole school prefer the Sports Club
Students who prefer Sports Club \(= 9\)
Total students surveyed \(= 40\)
\(P(Sports\, Club) = \frac{9}{40}\)
Applying this proportion to the whole school,
Estimated number \(= \frac{9}{40} × 800 = 180\)
Approximately \(180\) students in the whole school are likely to prefer the Sports Club.
Total students surveyed \(= 40\)
\(P(Sports\, Club) = \frac{9}{40}\)
Applying this proportion to the whole school,
Estimated number \(= \frac{9}{40} × 800 = 180\)
Approximately \(180\) students in the whole school are likely to prefer the Sports Club.
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Final Answer :
P(A random student from the sample prefers the Arts Club) \(= \frac{11}{40}\)
Estimated number of students in the whole school who prefer the Sports Club \(= \frac{9}{40}\)
Concept Note
A sample represents a smaller group from a larger population. If a sample is random and fair, we can use its proportion to estimate the values for the whole population.
In this question, \(\frac{9}{40}\) of surveyed students preferred the Sports Club, so we assumed the same proportion for all 800 students.