Oxford Cambridge and RSA
Examinations GCE Further
Mathematics B MEIY432/01:
Statistics minor
A Level
Question paper with marking scheme
(merged)
, Oxford Cambridge and RSA
Friday 16 June 2023 – Afternoon
A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Time allowed: 1 hour 15 minutes
* 9 9 7 0 7 1 6 3 5 8 *
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 2023 [M/508/5596] OCR is an exempt Charity
DC (ST/SG) 318818/5 Turn over
, 2
1 A fair spinner has ten sectors, labelled 1, 2, …, 10. In order to start a game, Kofi has to obtain an
8, 9 or 10 on the spinner.
(a) Find the probability that Kofi starts the game on the third spin. [2]
(b) Find the probability that Kofi takes at least 5 spins to start the game. [1]
(c) Determine the probability that the number of spins required to start the game is within 1
standard deviation of its mean. [5]
2 A company manufactures batches of twenty thousand tins which are subsequently filled with fruit.
The company tests tins from each batch to make sure that they are strong enough. The test is easy
and cheap to carry out, but when a tin has been tested it is no longer suitable for filling with fruit.
(a) (i) Explain why a sample size of 5 tins per batch may not be appropriate in this case. [1]
(ii) Explain why a sample size of 1000 tins per batch may not be appropriate in this case. [1]
The company tests a sample of 30 tins from each batch.
(b) Explain why it would not be sensible for the sample to consist of the final 30 tins produced in
a batch. [1]
(c) Give two features that the sample should have. [2]
© OCR 2023 Y432/01 Jun23
, 3
3 A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete
random variable X is the sum of the lowest and highest scores obtained.
3
(a) Show that P (X = 1) = 32 . [3]
The table below shows the probability distribution of X.
r 0 1 2 3 4 5 6
1 3 13 3 13 3 1
P (X = r) 64 32 64 8 64 32 64
(b) In this question you must show detailed reasoning.
Find each of the following.
• E(X )
• Var(X ) [4]
(c) The random variable Y represents the sum of 10 values of X.
(i) State a property of the 10 values of X that would make it possible to deduce the standard
deviation of Y. [1]
(ii) Given that this property holds, determine the standard deviation of Y. [2]
© OCR 2023 Y432/01 Jun23 Turn over
Examinations GCE Further
Mathematics B MEIY432/01:
Statistics minor
A Level
Question paper with marking scheme
(merged)
, Oxford Cambridge and RSA
Friday 16 June 2023 – Afternoon
A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Time allowed: 1 hour 15 minutes
* 9 9 7 0 7 1 6 3 5 8 *
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 2023 [M/508/5596] OCR is an exempt Charity
DC (ST/SG) 318818/5 Turn over
, 2
1 A fair spinner has ten sectors, labelled 1, 2, …, 10. In order to start a game, Kofi has to obtain an
8, 9 or 10 on the spinner.
(a) Find the probability that Kofi starts the game on the third spin. [2]
(b) Find the probability that Kofi takes at least 5 spins to start the game. [1]
(c) Determine the probability that the number of spins required to start the game is within 1
standard deviation of its mean. [5]
2 A company manufactures batches of twenty thousand tins which are subsequently filled with fruit.
The company tests tins from each batch to make sure that they are strong enough. The test is easy
and cheap to carry out, but when a tin has been tested it is no longer suitable for filling with fruit.
(a) (i) Explain why a sample size of 5 tins per batch may not be appropriate in this case. [1]
(ii) Explain why a sample size of 1000 tins per batch may not be appropriate in this case. [1]
The company tests a sample of 30 tins from each batch.
(b) Explain why it would not be sensible for the sample to consist of the final 30 tins produced in
a batch. [1]
(c) Give two features that the sample should have. [2]
© OCR 2023 Y432/01 Jun23
, 3
3 A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete
random variable X is the sum of the lowest and highest scores obtained.
3
(a) Show that P (X = 1) = 32 . [3]
The table below shows the probability distribution of X.
r 0 1 2 3 4 5 6
1 3 13 3 13 3 1
P (X = r) 64 32 64 8 64 32 64
(b) In this question you must show detailed reasoning.
Find each of the following.
• E(X )
• Var(X ) [4]
(c) The random variable Y represents the sum of 10 values of X.
(i) State a property of the 10 values of X that would make it possible to deduce the standard
deviation of Y. [1]
(ii) Given that this property holds, determine the standard deviation of Y. [2]
© OCR 2023 Y432/01 Jun23 Turn over
