OCR A Level Further Mathematics B (MEI)
Statistics Major(Y422/01) VERIFIED QP
AND MS
Oxford Cambridge and RSA
June – Afternoon
A Level Further Mathematics B (MEI)
Y422/01 Statistics Major
Time allowed: 2 hours 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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, OCR is an exempt Charity
Turn over
*1870418660*
,
, 2
Section A (34 marks)
1 A fair eight sided dice has its sides labelled 1, 2, …, 8. The random variable X represents the score
when the dice is rolled once.
(a) Find P(X 2 4). [1]
(b) Find each of the following.
• E(X)
• Var(X) [3]
The dice is rolled 3 times.
(c) Determine the exact probability that one of the scores is less than 4 and the other two are
greater than 4. [3]
2 At a toy factory, wooden blocks of approximate heights 20 mm, 30 mm and 50 mm are made in
red, yellow and green respectively. The heights of the blocks in mm are modelled by independent
random variables which are Normally distributed with means and standard deviations as shown in
the table.
Colour Mean Standard deviation
Red 20 0.8
Yellow 30 0.9
Green 50 1.2
In parts (a), (b) and (c), the blocks are selected randomly and independently of one another.
(a) Find the probability that the height of a red block is less than 19 mm. [1]
(b) A tower is made of 15 blocks stacked on top of each other consisting of 5 red blocks,
5 yellow blocks and 5 green blocks.
Determine the probability that the tower is at least 495 mm high. [4]
(c) Determine the probability that a tower made of 3 red blocks will be at least 1 mm higher than
a tower made of 2 yellow blocks. [3]
Statistics Major(Y422/01) VERIFIED QP
AND MS
Oxford Cambridge and RSA
June – Afternoon
A Level Further Mathematics B (MEI)
Y422/01 Statistics Major
Time allowed: 2 hours 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 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, OCR is an exempt Charity
Turn over
*1870418660*
,
, 2
Section A (34 marks)
1 A fair eight sided dice has its sides labelled 1, 2, …, 8. The random variable X represents the score
when the dice is rolled once.
(a) Find P(X 2 4). [1]
(b) Find each of the following.
• E(X)
• Var(X) [3]
The dice is rolled 3 times.
(c) Determine the exact probability that one of the scores is less than 4 and the other two are
greater than 4. [3]
2 At a toy factory, wooden blocks of approximate heights 20 mm, 30 mm and 50 mm are made in
red, yellow and green respectively. The heights of the blocks in mm are modelled by independent
random variables which are Normally distributed with means and standard deviations as shown in
the table.
Colour Mean Standard deviation
Red 20 0.8
Yellow 30 0.9
Green 50 1.2
In parts (a), (b) and (c), the blocks are selected randomly and independently of one another.
(a) Find the probability that the height of a red block is less than 19 mm. [1]
(b) A tower is made of 15 blocks stacked on top of each other consisting of 5 red blocks,
5 yellow blocks and 5 green blocks.
Determine the probability that the tower is at least 495 mm high. [4]
(c) Determine the probability that a tower made of 3 red blocks will be at least 1 mm higher than
a tower made of 2 yellow blocks. [3]
