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2024 Oxford Cambridge and RSA A Level Further Mathematics B (MEI) Y432/01 Statistics Minor ACTUAL QUESTION PAPER AND MARKING SCHEME (MERGED)$7.39
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OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 14 June 2024 – AfternoonA 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 AnswerBooklet. 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 begiven
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 is an exempt
,Charity
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, 2
1 When a footballer takes a penalty kick the result is that either a goal is scored or a goal is
notscored.
It is known that, on average, a certain footballer scores a goal on 85% of penalty kicks. During
one practice session, the footballer decides to take penalty kicks until a goal is not scored. You
may assume that the outcome of each penalty kick that the footballer takes is independent of
theoutcome of each other penalty kick.
The random variable representing the number of penalty kicks up to and including the first
penaltykick that does not result in a goal is denoted by X.
(a) State one further assumption that is necessary for X to be modelled by a Geometric
distribution. [1]
For the remainder of this question you may assume that this assumption is valid.
(b) Find each of the following.
• E(X)
• Var(X) [2]
(c) Find the probability that the footballer takes exactly 3 penalty kicks. [2]
(d) Find the probability that the footballer takes at least 5 penalty kicks. [2]
2 The sides of a fair 12-sided spinner are labelled 1, 2, ..., 12.
The spinner is spun and X is the random variable denoting the number on the side of the
spinnerthat it lands on.
(a) Suggest a suitable distribution to model X. You should state the value(s) of any parameter(s).
[2]
(b) Find each of the following.
• E(X)
• Var(X) [2]
You are given that E(X) is denoted by n and Var(X) is denoted by v 2 .
2 (X - n)
(c) Determine P c 2 1m. [3]
v
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