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Learn/ A Level Mathematics/ Past Papers/ 2022/ Oct/Nov 2022 /Paper 6 (Variant 2)

Probability & Statistics 2 — Variant 2

A Level Mathematics · 9709/62 · Oct/Nov 2022

Question Paper

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Mark Scheme

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Questions

3 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

3
1.6%1.6\% of adults in a certain town ride a bicycle. A random sample of 200200 adults from this town is selected.
3(a) [4]
Use a suitable approximating distribution to find the probability that more than 33 of these adults ride a bicycle.
3(b) [2]
Justify your approximating distribution.
5
XX is a random variable with distribution B(10,0.2)\mathrm{B}(10, 0.2). A random sample of 160160 values of XX is taken.
5(a) [3]
Find the approximate distribution of the sample mean, including the values of the parameters.
5(b) [3]
Hence find the probability that the sample mean is less than 1.81.8.
6
The masses, in grams, of small and large bags of flour have the distributions N(510,100)\mathrm{N}(510, 100) and N(1015,324)\mathrm{N}(1015, 324) respectively. André selects 44 small bags of flour and 22 large bags of flour at random.
6(a) [5]
Find the probability that the total mass of these 66 bags of flour is less than 41304130 g.
6(b) [5]
Find the probability that the total mass of the 44 small bags is more than the total mass of the 22 large bags.

Published by Cambridge Assessment International Education. Reproduced for study use.