Worked solution
Select thirty distinct students fairly
A school administrative manager wishes to interview a sample of 30 students from the entire population of 750 students on the quality of canteen food. Explain how simple random sampling can be carried out to choose the 30 students.
CJC · Lecture · Example 1
Define the frame and draw without replacement
Obtain a complete alphabetical list of all 750 students and number them 1 to 750. Generate 30 distinct integers uniformly without replacement from that range; interview the students with those numbers. Every size-30 subset then has probability , and every student has inclusion probability . A complete frame matters: choosing only friendly-looking students is the source’s contrasting non-random example.
Source calculator procedure
Use math → PROB → 8:randIntNoRep, set lower 1, upper 750, n 30 and press enter. Store the generated list with sto→, 2nd, 1 into L1. The source screen begins 22, 629, 464, 154, 739, 544, …; these are an illustration, not required choices. Repeating the procedure normally produces a different sample, but a repeat is possible: randomness does not guarantee a different list every time.
Common mistakes
The teacher stresses equal chance and independence. Equal-chance finite sampling without replacement has dependent selections; do not claim this procedure produces independent student identities. The iid model used later is a separate assumption.
Solution notes
Marked self-reading in both copies. The teacher’s page 2 reference to the H1 Math/2011/1/7 Examiner’s Report is retained as a source reference; that external report has not been reviewed. No marks printed.