Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · Oct/Nov 2022

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Questions

2 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.

2
The lengths of the rods produced by a company are normally distributed with mean 55.655.6 mm and standard deviation 1.21.2 mm.
2(a) [4]
In a random sample of 400400 of these rods, how many would you expect to have length less than 54.854.8 mm?
2(b) [3]
Find the probability that a randomly chosen rod produced by this company has a length that is within half a standard deviation of the mean.
3
Three fair 66-sided dice, each with faces marked 1,2,3,4,5,61, 2, 3, 4, 5, 6, are thrown at the same time repeatedly. The score on each throw is the sum of the numbers on the uppermost faces.
3(a) [3]
Find the probability that a score of 1717 or more is first obtained on the 66th throw.
3(b) [2]
Find the probability that a score of 1717 or more is obtained in fewer than 88 throws.

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