CAIE A-Level Mathematics 6.4.2 Sampling methods

CAIE A-Level Mathematics 6.4.2 Sampling methods
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise judging sampling methods, using random digits or dice fairly, and explaining when a chosen sample is biased or not random.

How this is tested

  • explain why unequal chances from random numbers make a sample non-random
  • use dice or random digits to allocate members with equal probability

Question 3

[Maximum number: 3]

Maroulla's calculator can generate random numbers between 0.000 and 0.999 inclusive, correct to 3 significant figures. She plans to use her calculator to choose a sample of members from the 851 members in her health club. She numbers the members from 1 to 851. Then she uses her calculator to generate some random numbers. She multiplies each random number by 851 and rounds up to the next whole number to give the number of a member in the sample. This is called a 'member number'.

Question 3(b)

(a)

Find all possible random numbers, correct to 3 decimal places, that would produce the following member numbers.

[ 2 ]

Question 3(b)(i)

(i)

A member number of 680 .

[ 1 ]

Question 3(b)(ii)

(ii)

A member number of 850 .

[ 1 ]

Question 3(c)

(b)

Explain briefly how your answers to part (b) show that Maroulla's method does not produce a random sample.

[ 1 ]