2025 OCR A Level Further Mathematics B (MEI) Y432/01 Statistics Minor
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon
A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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.
, © OCR 2025 [M/508/5596] OCR is an exempt Charity
DC (SL) 354112/3 Turn over
*1873515560*
, 2
1 A discrete random variable, X, has a Poisson distribution with mean 4.
(a) Write down the value of Var (X ). [1]
(b) Find P(X = 3). [1]
(c) Find P(X 2 3). [2]
Another discrete random variable, Y, which is independent of X, has a Poisson distribution with
mean 5.
(d) Find P(X + Y G 9). [2]
2 In an experiment, the speed of an object, v ms -1 , at time t seconds, is recorded at intervals of
10 seconds from t = 0 to t = 80.
The summary statistics are as follows.
n = 8, Rt = 280, Rt2 = 14000, Rv = 876.28, Rv2 = 133310.2, Rtv = 43190
A linear function of t is used as a model for v.
(a) By first determining the equation of an appropriate regression line, estimate the value of v
when t = 45. [3]
(b) Comment on the reliability of your estimate in part (a). [1]
(c) Explain why in this scenario it would be inappropriate to use a value of v to estimate a value
of t using any regression line. [1]
© OCR 2025 Y432/01 Jun25
, 3
3 An archer fires arrows one by one at a target until an arrow hits the target. The number of arrows
fired up to and including the arrow that hits the target is denoted by X. The archer considers using
a geometric model for the distribution of X.
(a) State two assumptions required for such a model to be appropriate. [2]
For the remainder of this question you may assume that a geometric model is appropriate for the
distribution of X.
The archer keeps records of the values of X. He collects a sample of these values and uses them to
estimate the variance of X.
(b) Give two features that the sample should have. [2]
The estimate of the variance of X calculated from the sample is 12.
(c) Determine an estimate of the probability that when the archer fires a single arrow at the
target, the arrow hits the target. [3]
(d) Use your answer to part (c) to write down an estimate of the expected number of arrows that
the archer must fire at the target up to and including the first arrow that hits the target. [1]
4 The discrete random variable, X, has a uniform distribution over the values {5, 6, ..., n}.
(a) In this question you must show detailed reasoning.
In part (a) you should assume that n = 24.
(i) Using the formula E(X) = / xi pi , determine the value of E(X) by direct calculation. [3]
(ii) Use the substitution Y = X - 4 and the given formula in the formulae booklet to
determine Var (X ). [2]
1
(iii) Show that P(X 2 E(X )) = . [1]
2
1
(b) A student states that P(X 2 E(X )) = for all n H 24.
2
Explain whether the student is correct. [1]
© OCR 2025 Y432/01 Jun25 Turn over
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon
A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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.
, © OCR 2025 [M/508/5596] OCR is an exempt Charity
DC (SL) 354112/3 Turn over
*1873515560*
, 2
1 A discrete random variable, X, has a Poisson distribution with mean 4.
(a) Write down the value of Var (X ). [1]
(b) Find P(X = 3). [1]
(c) Find P(X 2 3). [2]
Another discrete random variable, Y, which is independent of X, has a Poisson distribution with
mean 5.
(d) Find P(X + Y G 9). [2]
2 In an experiment, the speed of an object, v ms -1 , at time t seconds, is recorded at intervals of
10 seconds from t = 0 to t = 80.
The summary statistics are as follows.
n = 8, Rt = 280, Rt2 = 14000, Rv = 876.28, Rv2 = 133310.2, Rtv = 43190
A linear function of t is used as a model for v.
(a) By first determining the equation of an appropriate regression line, estimate the value of v
when t = 45. [3]
(b) Comment on the reliability of your estimate in part (a). [1]
(c) Explain why in this scenario it would be inappropriate to use a value of v to estimate a value
of t using any regression line. [1]
© OCR 2025 Y432/01 Jun25
, 3
3 An archer fires arrows one by one at a target until an arrow hits the target. The number of arrows
fired up to and including the arrow that hits the target is denoted by X. The archer considers using
a geometric model for the distribution of X.
(a) State two assumptions required for such a model to be appropriate. [2]
For the remainder of this question you may assume that a geometric model is appropriate for the
distribution of X.
The archer keeps records of the values of X. He collects a sample of these values and uses them to
estimate the variance of X.
(b) Give two features that the sample should have. [2]
The estimate of the variance of X calculated from the sample is 12.
(c) Determine an estimate of the probability that when the archer fires a single arrow at the
target, the arrow hits the target. [3]
(d) Use your answer to part (c) to write down an estimate of the expected number of arrows that
the archer must fire at the target up to and including the first arrow that hits the target. [1]
4 The discrete random variable, X, has a uniform distribution over the values {5, 6, ..., n}.
(a) In this question you must show detailed reasoning.
In part (a) you should assume that n = 24.
(i) Using the formula E(X) = / xi pi , determine the value of E(X) by direct calculation. [3]
(ii) Use the substitution Y = X - 4 and the given formula in the formulae booklet to
determine Var (X ). [2]
1
(iii) Show that P(X 2 E(X )) = . [1]
2
1
(b) A student states that P(X 2 E(X )) = for all n H 24.
2
Explain whether the student is correct. [1]
© OCR 2025 Y432/01 Jun25 Turn over
