surname names
Number Number
Pearson Edexcel GCE
In A Level Further Mathematics (9FM0) Paper 3B Further Statistics 1
■ ■
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 o r ball-po int pen.
• Fill If pencil is used fo r diagrams/sketches/graphs it must be dark (HB o r B).
in the boxes at the to p o f this page with yo ur 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
• Answers
– there may be more space than you need.
•• Values frowitho
You should show sufficient working to make your methods clear.
ut wo rking may no t gain full credit.
m statistical tables sho uld be quo ted in full. If a calculato r is used instead o f
•Information
the tables the value should be given to an equivalent degree of accuracy.
Inexact answers sho uld be given to three significant figures unless o therwise stated.
•• AThere
bo o klet ‘Mathematical Fo rmulae and Statistical Tables’ is pro vided.
• The
are 7 questio ns in this questio n paper. The to tal mark fo r this paper is 75.
– usemarks each as
this asfoar guide questio n are
to how muchshotime
wn in
tobrackets
spend on each question.
•Advice
Read each questio n carefully befo re yo u start to answer it.
•• Try to answer every questio n.
Check yo ur answers if yo u have time at the end. Turn over
,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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, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
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Question 1 continued
(Total for Question 1 is 6 marks)
Turn over
3
, 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
■■■■
Number Number
Pearson Edexcel GCE
In A Level Further Mathematics (9FM0) Paper 3B Further Statistics 1
■ ■
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 o r ball-po int pen.
• Fill If pencil is used fo r diagrams/sketches/graphs it must be dark (HB o r B).
in the boxes at the to p o f this page with yo ur 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
• Answers
– there may be more space than you need.
•• Values frowitho
You should show sufficient working to make your methods clear.
ut wo rking may no t gain full credit.
m statistical tables sho uld be quo ted in full. If a calculato r is used instead o f
•Information
the tables the value should be given to an equivalent degree of accuracy.
Inexact answers sho uld be given to three significant figures unless o therwise stated.
•• AThere
bo o klet ‘Mathematical Fo rmulae and Statistical Tables’ is pro vided.
• The
are 7 questio ns in this questio n paper. The to tal mark fo r this paper is 75.
– usemarks each as
this asfoar guide questio n are
to how muchshotime
wn in
tobrackets
spend on each question.
•Advice
Read each questio n carefully befo re yo u start to answer it.
•• Try to answer every questio n.
Check yo ur answers if yo u have time at the end. Turn over
,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)
Turn over
3
, 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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