AQA_2024: A-level Further Mathematics - Paper 3
Statistics
(Merged Question Paper and Marking Scheme)
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 3 Statistics
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
A‑ level Mathematics and A‑ level Further Mathematics. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
You must ensure you have the other optional Question Paper/Answer Book 2
for which you are entered (either Discrete or Mechanics). You will have
2 hours to complete both papers. 3
4
Instructions
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 5
Fill in the boxes at the top of this page.
6
Answer all questions.
You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages. 9
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do not want 10
to be marked.
TOTAL
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 50.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
,A-Level Further Mathematics: Paper 3 Statistics (Friday 7 June 2024)
Exam Preview Areas
This paper focuses on Advanced Statistical Methods, covering a range of topics related to probability theory,
distributions, and statistical analysis. Key areas usually include:
1. Probability:
Conditional Probability: Understanding how to calculate the probability of an event occurring given that
another event has already occurred.
Bayes' Theorem: Applying Bayes’ Theorem to revise probabilities based on new evidence.
2. Discrete and Continuous Distributions:
Binomial Distribution: Solving problems involving success/failure trials with fixed probabilities.
Poisson Distribution: Modelling the number of events occurring in fixed intervals of time or space.
Normal Distribution:
3. Estimation:
Confidence Intervals: Constructing and interpreting confidence intervals for population parameters, such
as mean and proportion.
Estimating Parameters: Using sample data to estimate population parameters, and understanding the
margin of error.
4. Hypothesis Testing:
Significance Tests: Conducting tests for population means and proportions using techniques such as t-
tests and z-tests, and interpreting P-values.
Chi-Square Tests:
5. Regression and Correlation:
Linear Regression: Fitting a line to bivariate data and interpreting the slope and intercept.
Correlation: Calculating and interpreting the correlation coefficient, assessing the strength and direction of
relationships between variables.
6. Experimental Design:
Sampling Methods: Understanding the different types of sampling techniques, including random, stratified,
and systematic sampling.
7. Advanced Data Analysis:
Analysis of Variance (ANOVA): Comparing the means of multiple groups to assess whether there are
significant differences.
This paper assesses your ability to apply advanced statistical methods to analyze data, interpret results, and draw
conclusions. You will need to use a range of statistical techniques for problem-solving, estimation, and hypothesis
testing in various contexts.
G/LM/Jun24/G4006/V6 7367/3S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The random variable X has a Poisson distribution with mean 16
Find the standard deviation of X
Circle your answer.
[1 mark]
4 8 16 256
2 The random variable T has an exponential distribution with mean 2
Find P(T ≤ 1.4)
Circle your answer.
[1 mark]
e–2.8 e– 0.7 1 – e– 0.7 1 – e–2.8
G/Jun24/7367/3S
, 3
Do not write
outside the
box
3 The continuous random variable Y has cumulative distribution function
– 10y2 + 10 y – 16 2≤y<5
{
F( y) = 2
9 9 9
1 y≥5
Find the median of Y
Circle your answer.
[1 mark]
10 – 3√ 2 7 10 + 3√ 2
2
2 2 2
Turn over for the next question
Turn over U
G/Jun24/7367/3S
, 4
Do not write
outside the
box
4 Research has shown that the mean number of volcanic eruptions on Earth each
day is 20
Sandra records 162 volcanic eruptions during a period of one week.
Sandra claims that there has been an increase in the mean number of volcanic
eruptions per week.
Test Sandra’s claim at the 5% level of significance.
[6 marks]
G/Jun24/7367/3S
, 5
Do not write
outside the
box
5 The continuous random variable X has probability density function
x
{
1 3
e 0 ≤ x ≤ In 27
6
f (x) =
0 otherwise
3
Show that the mean of X is (In 27 – 2)
2
[5 marks]
Turn over U
G/Jun24/7367/3S
, 6
Do not write
outside the
box
6 Over time it has been accepted that the mean retirement age for professional baseball
players is 29.5 years old.
Imran claims that the mean retirement age is no longer 29.5 years old.
He takes a random sample of 5 recently retired professional baseball players and
records their retirement ages, x. The results are
x = 152.1 and (x – x)2 = 7.81
6 (a) State an assumption that you should make about the distribution of the retirement ages
to investigate Imran’s claim.
[1 mark]
6 (b) Investigate Imran’s claim, using the 10% level of significance.
[8 marks]
G/Jun24/7367/3S
, 7
Do not write
outside the
box
Turn over for the next question
Turn over U
G/Jun24/7367/3S
, 8
Do not write
outside the
7 The random variable X has a discrete uniform distribution and takes values 1, 2, 3, …, n box
The random variable Y has probability distribution function
P(Y = y) =
{ 1
n
0
y = 13, 16, 19 ..., 3n + 10
otherwise
7 (a) State the variance of X
[1 mark]
7 (b) Hence find the variance of Y
Fully justify your answer.
[3 marks]
G/Jun24/7367/3S
Statistics
(Merged Question Paper and Marking Scheme)
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 3 Statistics
Friday 7 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
A‑ level Mathematics and A‑ level Further Mathematics. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
You must ensure you have the other optional Question Paper/Answer Book 2
for which you are entered (either Discrete or Mechanics). You will have
2 hours to complete both papers. 3
4
Instructions
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 5
Fill in the boxes at the top of this page.
6
Answer all questions.
You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages. 9
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do not want 10
to be marked.
TOTAL
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 50.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
,A-Level Further Mathematics: Paper 3 Statistics (Friday 7 June 2024)
Exam Preview Areas
This paper focuses on Advanced Statistical Methods, covering a range of topics related to probability theory,
distributions, and statistical analysis. Key areas usually include:
1. Probability:
Conditional Probability: Understanding how to calculate the probability of an event occurring given that
another event has already occurred.
Bayes' Theorem: Applying Bayes’ Theorem to revise probabilities based on new evidence.
2. Discrete and Continuous Distributions:
Binomial Distribution: Solving problems involving success/failure trials with fixed probabilities.
Poisson Distribution: Modelling the number of events occurring in fixed intervals of time or space.
Normal Distribution:
3. Estimation:
Confidence Intervals: Constructing and interpreting confidence intervals for population parameters, such
as mean and proportion.
Estimating Parameters: Using sample data to estimate population parameters, and understanding the
margin of error.
4. Hypothesis Testing:
Significance Tests: Conducting tests for population means and proportions using techniques such as t-
tests and z-tests, and interpreting P-values.
Chi-Square Tests:
5. Regression and Correlation:
Linear Regression: Fitting a line to bivariate data and interpreting the slope and intercept.
Correlation: Calculating and interpreting the correlation coefficient, assessing the strength and direction of
relationships between variables.
6. Experimental Design:
Sampling Methods: Understanding the different types of sampling techniques, including random, stratified,
and systematic sampling.
7. Advanced Data Analysis:
Analysis of Variance (ANOVA): Comparing the means of multiple groups to assess whether there are
significant differences.
This paper assesses your ability to apply advanced statistical methods to analyze data, interpret results, and draw
conclusions. You will need to use a range of statistical techniques for problem-solving, estimation, and hypothesis
testing in various contexts.
G/LM/Jun24/G4006/V6 7367/3S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The random variable X has a Poisson distribution with mean 16
Find the standard deviation of X
Circle your answer.
[1 mark]
4 8 16 256
2 The random variable T has an exponential distribution with mean 2
Find P(T ≤ 1.4)
Circle your answer.
[1 mark]
e–2.8 e– 0.7 1 – e– 0.7 1 – e–2.8
G/Jun24/7367/3S
, 3
Do not write
outside the
box
3 The continuous random variable Y has cumulative distribution function
– 10y2 + 10 y – 16 2≤y<5
{
F( y) = 2
9 9 9
1 y≥5
Find the median of Y
Circle your answer.
[1 mark]
10 – 3√ 2 7 10 + 3√ 2
2
2 2 2
Turn over for the next question
Turn over U
G/Jun24/7367/3S
, 4
Do not write
outside the
box
4 Research has shown that the mean number of volcanic eruptions on Earth each
day is 20
Sandra records 162 volcanic eruptions during a period of one week.
Sandra claims that there has been an increase in the mean number of volcanic
eruptions per week.
Test Sandra’s claim at the 5% level of significance.
[6 marks]
G/Jun24/7367/3S
, 5
Do not write
outside the
box
5 The continuous random variable X has probability density function
x
{
1 3
e 0 ≤ x ≤ In 27
6
f (x) =
0 otherwise
3
Show that the mean of X is (In 27 – 2)
2
[5 marks]
Turn over U
G/Jun24/7367/3S
, 6
Do not write
outside the
box
6 Over time it has been accepted that the mean retirement age for professional baseball
players is 29.5 years old.
Imran claims that the mean retirement age is no longer 29.5 years old.
He takes a random sample of 5 recently retired professional baseball players and
records their retirement ages, x. The results are
x = 152.1 and (x – x)2 = 7.81
6 (a) State an assumption that you should make about the distribution of the retirement ages
to investigate Imran’s claim.
[1 mark]
6 (b) Investigate Imran’s claim, using the 10% level of significance.
[8 marks]
G/Jun24/7367/3S
, 7
Do not write
outside the
box
Turn over for the next question
Turn over U
G/Jun24/7367/3S
, 8
Do not write
outside the
7 The random variable X has a discrete uniform distribution and takes values 1, 2, 3, …, n box
The random variable Y has probability distribution function
P(Y = y) =
{ 1
n
0
y = 13, 16, 19 ..., 3n + 10
otherwise
7 (a) State the variance of X
[1 mark]
7 (b) Hence find the variance of Y
Fully justify your answer.
[3 marks]
G/Jun24/7367/3S
