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Learn/ A Level Mathematics/ Past Papers/ 2021/ Oct/Nov 2021 /Paper 6 (Variant 2)

Probability & Statistics 2 — Variant 2

A Level Mathematics · 9709/62 · Oct/Nov 2021

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
The mass, in kilograms, of a block of cheese sold in a supermarket is denoted by the random variable MM. The masses of a random sample of 40 blocks are summarised as follows. n=40n = 40 Σm=20.50\Sigma m = 20.50 Σm2=10.7280\Sigma m^{2} = 10.7280
1(a) [3]
Calculate unbiased estimates of the population mean and variance of MM.
1(b) [3]
The price, $P\$P, of a block of cheese of mass MM kg is found using the formula P=11M+0.50P = 11M + 0.50. Find estimates of the population mean and variance of PP.
2
Andy and Jessica are doing a survey about musical preferences. They plan to choose a representative sample of six students from the 256 students at their college.
2(a) [1]
Andy suggests that they go to the music building during the lunch hour and choose six students at random from the students who are there. Give a reason why this method is unsatisfactory.
2(b) [2]
Jessica decides to use another method. She numbers all the students in the college from 1 to 256. Then she uses her calculator and generates the following random numbers. 204393204393 162007162007 204028204028 587119587119 207395207395 From these numbers, she obtains six student numbers. The first three of her student numbers are 204, 162 and 7. Continue Jessica's method to obtain the next three student numbers.
7
7(a)
The probability density function of the random variable XX is given by f(x)={kx(4−x)0⩽x⩽2,0otherwise,f(x) = \begin{cases} kx(4 - x) & 0 \leqslant x \leqslant 2, \\ 0 & \text{otherwise,} \end{cases} where kk is a constant.
7(a)(i) [3]
Show that k=316k = \frac{3}{16}.
7(a)(ii) [3]
Find E(X)\mathrm{E}(X).
7(b) [3]
The random variable YY has the following properties. YY takes values between 0 and 5 only. The probability density function of YY is symmetrical. Given that P(Y<a)=0.2\mathrm{P}(Y < a) = 0.2, find P(2.5<Y<5−a)\mathrm{P}(2.5 < Y < 5 - a) illustrating your method with a sketch on the axes provided.

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