Ex 7.2, 2

Transcript

Ex 7.2, 2 (i) 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? Given Data: Total students in the sample = 40 Science = 14, Arts = 11, Sports = 9, Debate = 6 Total students in the school (population) = 800 Let’s answer our questions now Now, P(art club) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑖𝑛𝑔 𝑎𝑟𝑡 𝑐𝑙𝑢𝑏)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒) = 𝟏𝟏/𝟒𝟎 Ex 7.2, 2 (ii) 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. (ii) Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club. First, we find probability the student prefers Sports club from the sample P(Sports Club) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑖𝑛𝑔 𝑆𝑝𝑜𝑟𝑡𝑠 𝐶𝑙𝑢𝑏)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑆𝑎𝑚𝑝𝑙𝑒) =𝟗/𝟒𝟎 Now, to estimate the number in the whole school, we multiply the sample probability by the total population (i.e. 800 students) Thus, Estimated Number of Students preferring Sports Clube = P(Sports Club) × Total population = 𝟗/𝟒𝟎 × 𝟖𝟎𝟎 = 9 × 20 = 180 Thus, we estimate that 180 students in the whole school prefer the Sports Club.