2025 OCR A Level Further Mathematics A Y542/01 Statistics
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon
A Level Further Mathematics A
Y542/01 Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
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 page 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 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [J/508/5510] OCR is an exempt Charity
DC (PQ) 357273/3 Turn over
*1920068128*
, 3
1 A set of 16 observations of the bivariate data (X, Y ) are summarised as follows.
n = 16 / x = 136 / y = 352 / x2 = 1496 / y2 = 9104 / xy = 3642
Determine an estimate of the value of y corresponding to x = 8.5. [4]
2 The number of trees of a particular species found in 1km2 of a forest can be modelled by the
distribution Po(m).
The forest consists of two regions, A and B.
In the region A, m = 4. The number of trees of this species in a randomly chosen area of 3km2 in
region A is denoted by X.
(a) Find P(16 1 X 1 20). [3]
In region B, m = 8. The number of trees of this species in a randomly chosen area of 3km2 in
region B is denoted by Y.
The random variable Z is defined by Z = X + Y . It may be assumed that X and Y are independent.
(b) Write down a formula for P(Z = z), in terms of z. [2]
(c) The average numbers of trees of this species in one square kilometre are not the same in
regions A and B.
Explain why the associated modelling assumption for the distribution of Z is nevertheless
valid. [1]
(d) Show that Y - X does not have a Poisson distribution. [1]
© OCR 2025 Y542/01 Jun25 Turn over
, 2
3 The length, in cm, of sand lizards when fully grown is a random variable which is known to have
the distribution N(13.2, 3.42).
Some scientists discover a colony of what they believe to be sand lizards in a remote location.
The scientists measure the lengths of a random sample of 50 fully grown lizards from this remote
location. The mean of this random sample is 14.02 cm. You may assume that the variance of the
length of lizards on the remote island is 3.42 cm2.
(a) Test, at the 5% significance level, whether the fully grown lizards in this location have a
mean length which is different from 13.2 cm. [7]
(b) Now suppose it is not known that the lengths are normally distributed.
(i) Explain why the Central Limit Theorem can be used in this context. [1]
(ii) State where in your test the Central Limit Theorem would be used. [1]
4 In this question you must show the parameters of any distributions you use.
The continuous random variable V has the distribution N(42, 32).
The continuous random variable W has the distribution N(48, 42).
The random variable X is the sum of 5 independent observations of V.
The random variable Y is the sum of 7 independent observations of W.
(a) Determine P(X + Y 2 560). [3]
(b) Determine the probability that X is less than 60% of Y. [4]
© OCR 2025 Y542/01 Jun25
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 6 June 2025 – Afternoon
A Level Further Mathematics A
Y542/01 Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
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 page 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 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [J/508/5510] OCR is an exempt Charity
DC (PQ) 357273/3 Turn over
*1920068128*
, 3
1 A set of 16 observations of the bivariate data (X, Y ) are summarised as follows.
n = 16 / x = 136 / y = 352 / x2 = 1496 / y2 = 9104 / xy = 3642
Determine an estimate of the value of y corresponding to x = 8.5. [4]
2 The number of trees of a particular species found in 1km2 of a forest can be modelled by the
distribution Po(m).
The forest consists of two regions, A and B.
In the region A, m = 4. The number of trees of this species in a randomly chosen area of 3km2 in
region A is denoted by X.
(a) Find P(16 1 X 1 20). [3]
In region B, m = 8. The number of trees of this species in a randomly chosen area of 3km2 in
region B is denoted by Y.
The random variable Z is defined by Z = X + Y . It may be assumed that X and Y are independent.
(b) Write down a formula for P(Z = z), in terms of z. [2]
(c) The average numbers of trees of this species in one square kilometre are not the same in
regions A and B.
Explain why the associated modelling assumption for the distribution of Z is nevertheless
valid. [1]
(d) Show that Y - X does not have a Poisson distribution. [1]
© OCR 2025 Y542/01 Jun25 Turn over
, 2
3 The length, in cm, of sand lizards when fully grown is a random variable which is known to have
the distribution N(13.2, 3.42).
Some scientists discover a colony of what they believe to be sand lizards in a remote location.
The scientists measure the lengths of a random sample of 50 fully grown lizards from this remote
location. The mean of this random sample is 14.02 cm. You may assume that the variance of the
length of lizards on the remote island is 3.42 cm2.
(a) Test, at the 5% significance level, whether the fully grown lizards in this location have a
mean length which is different from 13.2 cm. [7]
(b) Now suppose it is not known that the lengths are normally distributed.
(i) Explain why the Central Limit Theorem can be used in this context. [1]
(ii) State where in your test the Central Limit Theorem would be used. [1]
4 In this question you must show the parameters of any distributions you use.
The continuous random variable V has the distribution N(42, 32).
The continuous random variable W has the distribution N(48, 42).
The random variable X is the sum of 5 independent observations of V.
The random variable Y is the sum of 7 independent observations of W.
(a) Determine P(X + Y 2 560). [3]
(b) Determine the probability that X is less than 60% of Y. [4]
© OCR 2025 Y542/01 Jun25
