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Learn/ A Level Mathematics/ Past Papers/ 2021/ May/June 2021 /Paper 5 (Variant 3)

Probability & Statistics 1 — Variant 3

A Level Mathematics · 9709/53 · May/June 2021

Question Paper

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Mark Scheme

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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.

3
A sports club has a volleyball team and a hockey team. The heights of the 66 members of the volleyball team are summarised by Σx=1050\Sigma x = 1050 and Σx2=193700\Sigma x^{2} = 193700, where xx is the height of a member in cm. The heights of the 1111 members of the hockey team are summarised by Σy=1991\Sigma y = 1991 and Σy2=366400\Sigma y^{2} = 366400, where yy is the height of a member in cm.
3(a) [2]
Find the mean height of all 1717 members of the club.
3(b) [3]
Find the standard deviation of the heights of all 1717 members of the club.
4
Three fair six-sided dice, each with faces marked 1,2,3,4,5,61, 2, 3, 4, 5, 6, are thrown at the same time, repeatedly. For a single throw of the three dice, the score is the sum of the numbers on the top faces.
4(a) [3]
Find the probability that the score is 44 on a single throw of the three dice.
4(b) [3]
Find the probability that a score of 1818 is obtained for the first time on the 5th throw of the three dice.

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