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.
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.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. The discrete random variable X has the following probability distribution
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)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. The number of errors made by a secretary is modelled by a Poisson distribution with a
mean of 2.4 per 100 words.
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)
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.
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.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. The discrete random variable X has the following probability distribution
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)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. The number of errors made by a secretary is modelled by a Poisson distribution with a
mean of 2.4 per 100 words.
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)
