Oxford Cambridge and
RSA Examinations
GCEFurther
Mathematics AY532/01:
StatisticsAS Level
question paper and
marking scheme
(merged)
, Oxford Cambridge and RSA
Friday 19 May 2023 – Afternoon
AS Level Further Mathematics A
Y532/01 Statistics
Time allowed: 1 hour 15 minutes
* 9 9 7 4 9 6 5 0 9 4 *
You must have:
• the Printed Answer Booklet
QP
• the Formulae Booklet for AS Level Further
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
1 A radar device is used to detect flaws in motorway roads before they become dangerous. The
number of flaws in a 1 km stretch of motorway is denoted by X. It may be assumed that flaws
occur randomly.
(a) State two further assumptions that are necessary for X to be well modelled by a Poisson
distribution. [2]
Assume now that X can be modelled by the distribution Po(5.7).
(b) Determine the probability that in a randomly chosen stretch of motorway, of length 1 km,
there are between 8 and 11 flaws, inclusive. [2]
(c) Determine the probability that in two randomly chosen, non-overlapping, stretches of
motorway, each of length 5 km, there are at least 30 flaws in one stretch and fewer than
30 flaws in the other stretch.
[3]
2 A music lover has 30 CDs arranged in a random order in a line on a shelf. Of these CDs, 7 are
classed as Baroque, 10 as Classical and 13 as Romantic.
(a) Determine the probability that all 7 Baroque CDs are next to each other. [3]
(b) Determine the probability that, of the 10 CDs furthest to the left on the shelf, at least 6 are
Baroque. [4]
3 An insurance company collected data concerning the age, x years, of policy holders and the
average size of claim, £y thousand. The data is summarised as follows.
n = 32 / x = 1340 / y = 612 / x 2 = 64 282 / y 2 = 13 418 / xy = 27 794
(a) Find the variance of x. [1]
(b) Find the equation of the regression line of y on x. [2]
(c) Hence estimate the expected size of claim from a policy holder of age 48. [1]
Tom is aged 48. He claims that the range of the data probably does not include people of his age
because the mean age for the data is 41.875, and 48 is not close to this.
(d) Use your answer to part (a) to determine how likely it is that Tom’s claim is correct. [2]
(e) Comment on the reliability of your estimate in part (c). You should refer to the value of the
product-moment correlation coefficient for the data, which is 0.579 correct to 3 significant
figures. [2]
, 3
4 A discrete random variable W has the probability distribution shown in the following table, in
which a and b are constants.
w 58 59 60 61 62 63
P(W = w) a b 0.2 0.2 0.1 0.1
It is given that E(W - 60) = 0.15.
Determine the value of Var(4W - 60). [7]
5 A psychologist investigates the relationship between ‘openness’ and ‘creativity’ in adults.
Each member of a random sample of 15 adults is given two tests, one on openness and one on
creativity. Each test has a maximum score of 75. The results are given in the table.
Adult A B C D E F G H I J K L M N O
Openness, x 39 34 29 20 40 35 20 36 55 31 41 43 33 30 33
Creativity, y 59 34 17 29 49 46 45 54 60 38 46 35 43 56 34
n = 15 / x = 519 / y = 645 / x 2 = 19 033 / y 2 = 29 751 / xy = 23 034
(a) Use Pearson’s product-moment correlation coefficient to test, at the 5% significance level,
whether there is positive association between openness and creativity. [6]
(b) State what the value of Pearson’s product-moment correlation coefficient shows about a
scatter diagram illustrating the data. [2]
(c) A student suggests that there is a way to obtain a more accurate measure of the correlation.
Before carrying out the test it would be better to standardise the test scores so that they have
the same mean and variance.
Explain whether you agree with this suggestion. [1]
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