2024 PEARSON EDEXCEL GCE A LEVEL FURTHER MATHEMATICS 9FMO/3B PAPER 3B MERGED QUESTIOIN
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3B: Further Statistics 1
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
•• Values fromwithout
should show sufficient working to make your methods clear.
Answers working may not gain full credit.
statistical tables should be quoted in full. If a calculator is used instead of
•Information
the tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
are 7 questions in this question paper. The total mark for this paper is 75.
The
– use marks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end.
Turn over
P72797A
©2024 Pearson Education Ltd.
F:1/1/1/1/
,1. The discrete random variable X has the following probability distribution
DO NOT WRITE IN THIS AREA
x –1 0 1 3 5
P(X = x) 0.2 0.1 0.2 0.25 0.25
(a) Find Var(X )
(3)
(b) Find Var(X 2)
(3)
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DO NOT WRITE IN THIS AREA
2
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Question 1 continued
(Total for Question 1 is 6 marks)
3
Turn over
, 2. The number of errors made by a secretary is modelled by a Poisson distribution with a
mean of 2.4 per 100 words.
DO NOT WRITE IN THIS AREA
A 100‑word piece of work completed by the secretary is selected at random.
(a) Find the probability that
(i) there are exactly 3 errors,
(ii) there are fewer than 2 errors.
(2)
After a long holiday, a randomly selected piece of work containing 250 words
completed by the secretary is examined to see if the rate of errors has changed.
(b) Stating your hypotheses clearly, and using a 5% level of significance, find the
critical region for a suitable test.
(4)
(c) Find P(Type I error) for the test in part (b)
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
■■■■
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3B: Further Statistics 1
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
•• Values fromwithout
should show sufficient working to make your methods clear.
Answers working may not gain full credit.
statistical tables should be quoted in full. If a calculator is used instead of
•Information
the tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
are 7 questions in this question paper. The total mark for this paper is 75.
The
– use marks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end.
Turn over
P72797A
©2024 Pearson Education Ltd.
F:1/1/1/1/
,1. The discrete random variable X has the following probability distribution
DO NOT WRITE IN THIS AREA
x –1 0 1 3 5
P(X = x) 0.2 0.1 0.2 0.25 0.25
(a) Find Var(X )
(3)
(b) Find Var(X 2)
(3)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
■■■■
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
(Total for Question 1 is 6 marks)
3
Turn over
, 2. The number of errors made by a secretary is modelled by a Poisson distribution with a
mean of 2.4 per 100 words.
DO NOT WRITE IN THIS AREA
A 100‑word piece of work completed by the secretary is selected at random.
(a) Find the probability that
(i) there are exactly 3 errors,
(ii) there are fewer than 2 errors.
(2)
After a long holiday, a randomly selected piece of work containing 250 words
completed by the secretary is examined to see if the rate of errors has changed.
(b) Stating your hypotheses clearly, and using a 5% level of significance, find the
critical region for a suitable test.
(4)
(c) Find P(Type I error) for the test in part (b)
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
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