2025 OCR A Level Further Mathematics B (MEI) Y422/01 Statistics Major Combined
Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – 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 2025 [H/508/5594] OCR is an exempt Charity
DC (ST/FC) 351650/5 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]
© OCR 2025 Y422/01 Jun25
, 3
3 Potatoes are sold in sacks of nominal weight 25 kg. As part of a trading standards check, a
random sample of 50 sacks from a large batch is selected and software is used to produce a 95%
confidence interval for the mean weight of potatoes per sack. An extract from the software is
shown below.
Sample Mean 24.878
Standard Deviation 0.5664
Standard Error 0.0801
Sample Size 50
Confidence Level 0.95
Interval 24.878 ± 0.157
(a) Show how the standard error was calculated. [1]
(b) State the confidence interval in the form a 1 n 1 b. [1]
(c) Explain whether the confidence interval suggests that the mean weight of potatoes per sack is
different from 25 kg. [1]
(d) Determine whether your conclusion to part (c) would have been different if the confidence
level had been 90%. [4]
4 Gabi is practising basketball. On each attempt to score a basket, the probability that Gabi scores is
modelled as 0.4. It is assumed that each attempt is independent of previous attempts. The number
of attempts which Gabi takes in order to score a basket for the first time is denoted by the random
variable X.
(a) (i) Calculate P(X = 5). [1]
(ii) Calculate P(X 25). [1]
(b) Determine the probability that X is within one standard deviation of its mean. [5]
(c) Determine the probability that Gabi scores at least 5 baskets in 20 attempts. [2]
(d) Determine the probability that Gabi scores the 5th basket on their 20th attempt. [2]
(e) Comment on the validity of the assumption that on each attempt to score a basket, the
probability that Gabi scores is 0.4, independent of previous attempts. [1]
© OCR 2025 Y422/01 Jun25 Turn over
Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 13 June 2025 – 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 2025 [H/508/5594] OCR is an exempt Charity
DC (ST/FC) 351650/5 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]
© OCR 2025 Y422/01 Jun25
, 3
3 Potatoes are sold in sacks of nominal weight 25 kg. As part of a trading standards check, a
random sample of 50 sacks from a large batch is selected and software is used to produce a 95%
confidence interval for the mean weight of potatoes per sack. An extract from the software is
shown below.
Sample Mean 24.878
Standard Deviation 0.5664
Standard Error 0.0801
Sample Size 50
Confidence Level 0.95
Interval 24.878 ± 0.157
(a) Show how the standard error was calculated. [1]
(b) State the confidence interval in the form a 1 n 1 b. [1]
(c) Explain whether the confidence interval suggests that the mean weight of potatoes per sack is
different from 25 kg. [1]
(d) Determine whether your conclusion to part (c) would have been different if the confidence
level had been 90%. [4]
4 Gabi is practising basketball. On each attempt to score a basket, the probability that Gabi scores is
modelled as 0.4. It is assumed that each attempt is independent of previous attempts. The number
of attempts which Gabi takes in order to score a basket for the first time is denoted by the random
variable X.
(a) (i) Calculate P(X = 5). [1]
(ii) Calculate P(X 25). [1]
(b) Determine the probability that X is within one standard deviation of its mean. [5]
(c) Determine the probability that Gabi scores at least 5 baskets in 20 attempts. [2]
(d) Determine the probability that Gabi scores the 5th basket on their 20th attempt. [2]
(e) Comment on the validity of the assumption that on each attempt to score a basket, the
probability that Gabi scores is 0.4, independent of previous attempts. [1]
© OCR 2025 Y422/01 Jun25 Turn over
