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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
Values from statistical tables should be quoted in full. If a calculator is used instead
of 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.
• There are 7 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
•
Turn over
Check your answers if you have time at the end.
,1. Irina is practising her serves in badminton and counts the number of her serves that are
faults. She finds that 15% of her serves are faults.
Assuming that each serve is independent,
(a) find the probability that
(i) Irina’s 4th fault comes on her 20th serve,
(2)
(ii) in 18 serves, Irina has 4 faults.
(2)
With practice, Irina reduces her proportion of faults, p, so that the mean number of
serves until her 4th fault is at least 32
(b) Find the maximum value of p
(3)
2
■■■■
,Question 1 continued
(Total for Question 1 is 7 marks)
3
■■■■ Turn over
, 2. The discrete random variable X has probability distribution
x –1 a b
1 1 1
P(X = x)
2 4 4
where a and b are positive constants.
(a) Find an expression for E(X ) in terms of a and b
(2)
The discrete random variable Y is defined as Y = a + bX
1 5
Given that Var(Y ) = Var(X ) and E(Y ) =
4 16
(b) find the value of E(X )
(7)
4
■■■■
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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
Values from statistical tables should be quoted in full. If a calculator is used instead
of 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.
• There are 7 questions in this question paper. The total mark for this paper is 75.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
•
Turn over
Check your answers if you have time at the end.
,1. Irina is practising her serves in badminton and counts the number of her serves that are
faults. She finds that 15% of her serves are faults.
Assuming that each serve is independent,
(a) find the probability that
(i) Irina’s 4th fault comes on her 20th serve,
(2)
(ii) in 18 serves, Irina has 4 faults.
(2)
With practice, Irina reduces her proportion of faults, p, so that the mean number of
serves until her 4th fault is at least 32
(b) Find the maximum value of p
(3)
2
■■■■
,Question 1 continued
(Total for Question 1 is 7 marks)
3
■■■■ Turn over
, 2. The discrete random variable X has probability distribution
x –1 a b
1 1 1
P(X = x)
2 4 4
where a and b are positive constants.
(a) Find an expression for E(X ) in terms of a and b
(2)
The discrete random variable Y is defined as Y = a + bX
1 5
Given that Var(Y ) = Var(X ) and E(Y ) =
4 16
(b) find the value of E(X )
(7)
4
■■■■
