Exam (elaborations)
OCR AS Level Further Mathematics B (MEI) Y412/01 Statistics a June 2024
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OCR AS Level Further Mathematics B (MEI) Y412/01 Statistics a June 2024
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Oxford Cambridge and RSAFriday 7 June 2024 – Afternoon
AS Level Further Mathematics B (MEI)
Y412/01 Statistics a
Time allowed: 1 hour 15 minutes
* 1 4 1 2 4 9 6 4 0 0 *
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 2024 [F/508/5554] OCR is an exempt Charity
DC (PQ) 334974/3 Turn over
, 2
1 The probability distribution for a discrete random variable X is given in the table below.
x 0 1 2 3
P (X = x) 2c 3c 0.5 - c c
(a) Find the value of c. [2]
(b) Find the value of each of the following.
• E(X )
• Var(X ) [3]
The random variable Y is defined by Y = 2X - 3.
(c) Find the value of each of the following.
• E(Y )
• Var(Y ) [2]
2 In a game of chance there are 32 slots, numbered 1 to 32, and on each turn a ball lands in one of
them. You may assume that the process is completely random.
You are given that X is the random variable denoting the number of the slot that the ball lands in
on a given turn.
(a) Suggest a suitable distribution to model X. You should state the value(s) of any parameter(s).
[2]
(b) Write down P (X = 7) . [1]
Players of the game start with a score of 0. On each turn a player may choose to play the game by
selecting a number. If the ball lands in the slot with that number then 15 is added to the player’s
score. Otherwise, the player’s score is reduced by 1. A player’s score may become negative.
A player decides to play the game, selecting the number 7 on each turn, until the ball lands in the
slot numbered 7.
You are given that Y is the random variable denoting the number of turns up to and including the
turn in which the ball lands in the slot numbered 7.
(c) Determine P (Y G 15) . [3]
(d) Determine the player’s expected final score. [3]
© OCR 2024 Y412/01 Jun24
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