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Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · Oct/Nov 2020

Question Paper

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Mark Scheme

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Questions

2 of 6 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
A bag contains 55 red balls and 33 blue balls. Sadie takes 33 balls at random from the bag, without replacement. The random variable XX represents the number of red balls that she takes.
2(a) [2]
Show that the probability that Sadie takes exactly 11 red ball is 1556\frac{15}{56}.
2(b) [3]
Draw up the probability distribution table for XX.
2(c) [2]
Given that E(X)=158\mathrm{E}(X) = \frac{15}{8}, find Var(X)\mathrm{Var}(X).
3
Pia runs 22 km every day and her times in minutes are normally distributed with mean 10.110.1 and standard deviation 1.31.3.
3(a) [3]
Find the probability that on a randomly chosen day Pia takes longer than 11.311.3 minutes to run 22 km.
3(b) [3]
On 75%75\% of days, Pia takes longer than tt minutes to run 22 km. Find the value of tt.
3(c) [3]
On how many days in a period of 9090 days would you expect Pia to take between 8.98.9 and 11.311.3 minutes to run 22 km?

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