A Level Further Mathematics B (MEI)
Y432 Statistics Minor
Sample Question Paper Version 3.0
Date – Morning/Afternoon
Time allowed: 1 hour 15 minutes
You must have:
• Printed Answer Booklet
• Formulae Further Mathematics B (MEI)
You may use:
• a scientific or graphical calculator
* 0 0 0 0 0 0 *
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. Additional paper may be used if necessary but you must clearly show your candidate
number, centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total number of marks for this paper is 60.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Booklet consists of 12 pages. The Question Paper consists of 8 pages.
© OCR 2025 Y432 Turn over
603/1364/X B10045/4.4
, 2
Answer all the questions.
1 A darts player is trying to hit the bullseye on a dart board. On each throw the probability that she hits it is
0.05, independently of any other throw.
(i) Find the probability that she hits the bullseye for the first time on her 10th throw. [2]
(ii) Find the probability that she does not hit the bullseye in her first 10 throws. [1]
(iii) Write down the expected number of throws which it takes her to hit the bullseye for the first time.
[1]
2 The number of televisions of a particular model sold per week at a retail store can be modelled by a random
variable X with the probability function shown in the table.
x 0 1 2 3 4
P( X = x) 0.05 0.2 0.5 0.2 0.05
(i) (A) Explain why E( X ) = 2. [1]
(B) Find Var( X ) . [3]
(ii) The profit, measured in pounds made in a week, on the sales of this model of television is given by Y,
where Y = 250 X − 80 .
Find
• E(Y ) and
• Var(Y ) . [2]
The remote controls for the televisions are quality tested by the manufacturer to see how long they last
before they fail.
(iii) Explain why it would be inappropriate to test all the remote controls in this way. [1]
(iv) State an advantage of using random sampling in this context. [1]
© OCR 2025 Y432
, 3
3 A website awards a random number of loyalty points each time a shopper buys from it. The shopper gets a
whole number of points between 0 and 10 (inclusive). Each possibility is equally likely, each time the
shopper buys from the website. Awards of points are independent of each other.
(i) Let X be the number of points gained after shopping once.
Find
• the mean of X
• the variance of X. [3]
(ii) Let Y be the number of points gained after shopping twice.
Find
• the mean of Y
• the variance of Y. [3]
(iii) Find the probability of the most likely number of points gained after shopping twice. Justify your
answer. [4]
4 (i) State the conditions under which the Poisson distribution is an appropriate model for the number of
emails received by one person in a day. [2]
Jane records the number of junk emails which she receives each day. During working hours (9am to 5pm,
Monday to Friday) the mean number of junk emails is 7.4 per day. Outside working hours (5pm to 9am),
the mean number of junk emails is 0.3 per hour.
For the remainder of this question, you should assume that Poisson models are appropriate for the number
of junk emails received during each of “working hours” and “outside working hours”.
(ii) Find the probability that the number of junk emails which she receives between 9am and 5pm on a
Monday is
(A) exactly 10, [1]
(B) at least 10. [2]
(iii) (A) What assumption must you make to calculate the probability that the number of junk emails
which she receives from 9am Monday to 9am Tuesday is at most 20? [1]
(B) Find the probability. [2]
© OCR 2025 Y432 Turn over
, 4
5 Each contestant in a talent competition is given a score out of 20 by a judge. The organisers suspect that the
judge’s scores are associated with the age of the contestant. Table 5.1 and the scatter diagram in Fig. 5.2
show the scores and ages of a random sample of 7 contestants.
Contestant A B C D E F G
Age 66 51 39 29 9 22 14
Score 12 11 15 17 16 18 9
Table 5.1
20
Score
18
16
14
12
10
8
6
4
2
0
0 10 20 30 40 50 60 70
Age
Fig. 5.2
Contestant G did not finish her performance, so it is decided to remove her data.
(i) Spearman's rank correlation coefficient between age and score, including all 7 contestants, is −0.25.
Explain why Spearman's rank correlation coefficient becomes more negative when the data for
contestant G is removed. [1]
(ii) Calculate Spearman's rank correlation coefficient for the 6 remaining contestants. [3]
(iii) Using this value of Spearman’s rank correlation coefficient, carry out a hypothesis test at the 5% level
to investigate whether there is any association between age and score. [5]
(iv) Briefly explain why it may be inappropriate to carry out a hypothesis test based on Pearson's product
moment correlation coefficient using these data. [1]
© OCR 2025 Y432
Y432 Statistics Minor
Sample Question Paper Version 3.0
Date – Morning/Afternoon
Time allowed: 1 hour 15 minutes
You must have:
• Printed Answer Booklet
• Formulae Further Mathematics B (MEI)
You may use:
• a scientific or graphical calculator
* 0 0 0 0 0 0 *
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. Additional paper may be used if necessary but you must clearly show your candidate
number, centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total number of marks for this paper is 60.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Booklet consists of 12 pages. The Question Paper consists of 8 pages.
© OCR 2025 Y432 Turn over
603/1364/X B10045/4.4
, 2
Answer all the questions.
1 A darts player is trying to hit the bullseye on a dart board. On each throw the probability that she hits it is
0.05, independently of any other throw.
(i) Find the probability that she hits the bullseye for the first time on her 10th throw. [2]
(ii) Find the probability that she does not hit the bullseye in her first 10 throws. [1]
(iii) Write down the expected number of throws which it takes her to hit the bullseye for the first time.
[1]
2 The number of televisions of a particular model sold per week at a retail store can be modelled by a random
variable X with the probability function shown in the table.
x 0 1 2 3 4
P( X = x) 0.05 0.2 0.5 0.2 0.05
(i) (A) Explain why E( X ) = 2. [1]
(B) Find Var( X ) . [3]
(ii) The profit, measured in pounds made in a week, on the sales of this model of television is given by Y,
where Y = 250 X − 80 .
Find
• E(Y ) and
• Var(Y ) . [2]
The remote controls for the televisions are quality tested by the manufacturer to see how long they last
before they fail.
(iii) Explain why it would be inappropriate to test all the remote controls in this way. [1]
(iv) State an advantage of using random sampling in this context. [1]
© OCR 2025 Y432
, 3
3 A website awards a random number of loyalty points each time a shopper buys from it. The shopper gets a
whole number of points between 0 and 10 (inclusive). Each possibility is equally likely, each time the
shopper buys from the website. Awards of points are independent of each other.
(i) Let X be the number of points gained after shopping once.
Find
• the mean of X
• the variance of X. [3]
(ii) Let Y be the number of points gained after shopping twice.
Find
• the mean of Y
• the variance of Y. [3]
(iii) Find the probability of the most likely number of points gained after shopping twice. Justify your
answer. [4]
4 (i) State the conditions under which the Poisson distribution is an appropriate model for the number of
emails received by one person in a day. [2]
Jane records the number of junk emails which she receives each day. During working hours (9am to 5pm,
Monday to Friday) the mean number of junk emails is 7.4 per day. Outside working hours (5pm to 9am),
the mean number of junk emails is 0.3 per hour.
For the remainder of this question, you should assume that Poisson models are appropriate for the number
of junk emails received during each of “working hours” and “outside working hours”.
(ii) Find the probability that the number of junk emails which she receives between 9am and 5pm on a
Monday is
(A) exactly 10, [1]
(B) at least 10. [2]
(iii) (A) What assumption must you make to calculate the probability that the number of junk emails
which she receives from 9am Monday to 9am Tuesday is at most 20? [1]
(B) Find the probability. [2]
© OCR 2025 Y432 Turn over
, 4
5 Each contestant in a talent competition is given a score out of 20 by a judge. The organisers suspect that the
judge’s scores are associated with the age of the contestant. Table 5.1 and the scatter diagram in Fig. 5.2
show the scores and ages of a random sample of 7 contestants.
Contestant A B C D E F G
Age 66 51 39 29 9 22 14
Score 12 11 15 17 16 18 9
Table 5.1
20
Score
18
16
14
12
10
8
6
4
2
0
0 10 20 30 40 50 60 70
Age
Fig. 5.2
Contestant G did not finish her performance, so it is decided to remove her data.
(i) Spearman's rank correlation coefficient between age and score, including all 7 contestants, is −0.25.
Explain why Spearman's rank correlation coefficient becomes more negative when the data for
contestant G is removed. [1]
(ii) Calculate Spearman's rank correlation coefficient for the 6 remaining contestants. [3]
(iii) Using this value of Spearman’s rank correlation coefficient, carry out a hypothesis test at the 5% level
to investigate whether there is any association between age and score. [5]
(iv) Briefly explain why it may be inappropriate to carry out a hypothesis test based on Pearson's product
moment correlation coefficient using these data. [1]
© OCR 2025 Y432
