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Learn/ A Level Mathematics/ Past Papers/ 2022/ Oct/Nov 2022 /Paper 6 (Variant 3)

Probability & Statistics 2 — Variant 3

A Level Mathematics · 9709/63 · 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.

1 [3]
The heights, in metres, of a random sample of 1010 mature trees of a certain variety are given below. 5.9,6.5,6.7,5.9,6.9,6.0,6.4,6.2,5.8,5.85.9, 6.5, 6.7, 5.9, 6.9, 6.0, 6.4, 6.2, 5.8, 5.8 Find unbiased estimates of the population mean and variance of the heights of all mature trees of this variety.
3
Drops of water fall randomly from a leaking tap at a constant average rate of 5.25.2 per minute.
3(a) [3]
Find the probability that at least 33 drops fall during a randomly chosen 3030-second period.
3(b) [4]
Use a suitable approximating distribution to find the probability that at least 650650 drops fall during a randomly chosen 22-hour period.
5
A builders' merchant sells stones of different sizes.
5(a) [3]
The masses of size AA stones have standard deviation 66 grams. The mean mass of a random sample of 200200 size AA stones is 4545 grams. Find a 95%95\% confidence interval for the population mean mass of size AA stones.
5(b) [4]
The masses of size BB stones have standard deviation 1111 grams. Using a random sample of size 200200, an α%\alpha\% confidence interval for the population mean mass is found to have width 44 grams. Find α\alpha.

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