StudentAid
HomeLearn
9th Class10th Class11th Class12th ClassCambridge past papersBrowse everything
Attendance
Class attendanceVisitor register
For schoolsFor driversFor parentsBook a demo
Learn/ A Level Mathematics/ Past Papers/ 2021/ Feb/March 2021 /Paper 6 (Variant 2)

Probability & Statistics 2 — Variant 2

A Level Mathematics · 9709/62 · Feb/March 2021

Question Paper

PDF · 106 KB · 12 pages

Mark Scheme

PDF · 306 KB · 11 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

4 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.

1
A construction company notes the time, tt days, that it takes to build each house of a certain design. The results for a random sample of 60 such houses are summarised as follows. Σt=4820\Sigma t = 4820 Σt2=392050\Sigma t^{2} = 392050
1(a) [6]
Calculate a 98% confidence interval for the population mean time.
1(b) [1]
Explain why it was necessary to use the Central Limit theorem in part (a).
3
An architect wishes to investigate whether the buildings in a certain city are higher, on average, than buildings in other cities. He takes a large random sample of buildings from the city and finds the mean height of the buildings in the sample. He calculates the value of the test statistic, zz, and finds that z=2.41z = 2.41.
3(a) [1]
Explain briefly whether he should use a one-tail test or a two-tail test.
3(b) [3]
Carry out the test at the 1% significance level.
4
On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by XX.
4(a) [1]
State the distribution of XX, giving the values of any parameters.
4(b) [2]
State an approximating distribution for XX, giving the values of any parameters.
4(c)
Use this approximating distribution to find each of the following.
4(c)(i) [2]
P(X=4)\mathrm{P}(X = 4).
4(c)(ii) [2]
P(2⩽X⩽4)\mathrm{P}(2 \leqslant X \leqslant 4).
4(d) [3]
Use a suitable approximating distribution to find the probability that, in a random sample of 700 microchips, there will be at least 1 faulty one.
5
The volumes, in litres, of juice in large and small bottles have the distributions N(5.10,0.0102)\mathrm{N}(5.10, 0.0102) and N(2.51,0.0036)\mathrm{N}(2.51, 0.0036) respectively.
5(a) [5]
Find the probability that the total volume of juice in 3 randomly chosen large bottles and 4 randomly chosen small bottles is less than 25.525.5 litres.
5(b) [5]
Find the probability that the volume of juice in a randomly chosen large bottle is at least twice the volume of juice in a randomly chosen small bottle.

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