A survey is conducted at a school where a random sample of 40 students is asked about their favourite Club. Class 9

A survey is conducted at a school where a random sample of 40 students is asked about their favourite Club. Class 9

Question 1.

A survey is conducted at a school where a random sample of 40 students is asked about their favourite Club. The responses are: Class 9

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:

i. Total number of students in sample = 40

Students who prefer Arts Club = 11

$=\frac{\text { Students who prefer Arts Club }}{\text { Total number of students in sample }}$

= $\frac{11}{40}$

ii. Students who prefer Sports Club in sample = 9

P(Student prefers Sports Club)

$=\frac{\text { Students who prefers Sports Club }}{\text { Total number of students in sample }}=\frac{9}{40}$

∴ Estimated number of students in whole school who prefer Sports Club

= $\frac{9}{40}$ × 800

= 180

∴ 180 students are likely to prefer Sports Club.