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Learn/ A Level Mathematics/ Past Papers/ 2020/ May/June 2020 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · May/June 2020

Question Paper

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Mark Scheme

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Questions

5 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]
For nn values of the variable xx, it is given that Σ(x−50)=144\Sigma(x - 50) = 144 and Σx=944\Sigma x = 944. Find the value of nn.
4
Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution with mean 4040 m and standard deviation 1212 m. Trees with a height of less than 2525 m are classified as short.
4(a) [3]
Find the probability that a randomly chosen tree is classified as short. Of the trees that are classified as tall or medium, one third are tall and two thirds are medium.
4(b) [2]
Show that the probability that a randomly chosen tree is classified as tall is 0.2980.298, correct to 3 decimal places.
4(c) [3]
Find the height above which trees are classified as tall.
5
A fair three-sided spinner has sides numbered 1,2,31, 2, 3. A fair five-sided spinner has sides numbered 1,1,2,2,31, 1, 2, 2, 3. Both spinners are spun once. For each spinner, the number on the side on which it lands is noted. The random variable XX is the larger of the two numbers if they are different, and their common value if they are the same.
5(a) [2]
Show that P(X=3)=715\mathrm{P}(X = 3) = \frac{7}{15}.
5(b) [3]
Draw up the probability distribution table for XX.
5(c) [3]
Find E(X)\mathrm{E}(X) and Var(X)\mathrm{Var}(X).
6
6(a) [2]
Find the number of different ways in which the 1010 letters of the word SUMMERTIME can be arranged so that there is an E at the beginning and an E at the end.
6(b) [4]
Find the number of different ways in which the 1010 letters of the word SUMMERTIME can be arranged so that the Es are not together.
6(c) [3]
Four letters are selected from the 1010 letters of the word SUMMERTIME. Find the number of different selections if the four letters include at least one M and exactly one E.
7
On any given day, the probability that Moena messages her friend Pasha is 0.720.72.
7(a) [3]
Find the probability that for a random sample of 1212 days Moena messages Pasha on no more than 99 days.
7(b) [1]
Moena messages Pasha on 1 January. Find the probability that the next day on which she messages Pasha is 5 January.
7(c) [5]
Use an approximation to find the probability that in any period of 100100 days Moena messages Pasha on fewer than 6464 days.

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