PEARSON EDEXCEL INTERNATIONAL A LEVEL STATISTICS 2 COPY
PEARSON EDEXCEL INTERNATIONAL A LEVEL
STATISTICS 2 COPY Student Book
Series Editors: Joe Skrakowski and Harry Smith Authors: Greg Attwood, Tom Begley, Ian Bettison, Alan Clegg, Martin Crozier, Gill
E Dyer, Jane Dyer, Keith Gallick, Susan Hooker, Michael Jennings, John Kinoulty,
Mohammed Ladak, Guilherme Frederico Lima, Jean Littlewood, Bronwen Moran,
L James Nicholson, Su Nicholson, Laurence Pateman, Keith Pledger, Joe Skrakowski, SAMP Harry Smith
Published by Pearson Education Limited, 80 Strand, London, WC2R 0RL.
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First published 2019
22 21 20 19 10 9 8 7 6 5 4 3 2 1
British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library
ISBN 978 1 292245 17 1
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The authors and publisher would like to thank the following individuals and organisations for permission to reproduce photographs:
P To be updated: : Pavlovska Yevheniia 1, katjen 35, TK Kurikawa
87, Sergey Mironov 102, Shaiith 112; Science Photo Library: ALAN DYER/ VWPICS 17; 123RF: Viparat Kluengsuwanchai 49
Cover images: Front: Getty Images: Werner Van Steen Inside front cover: : Dmitry Lobanov
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CONTENTS
iii
COURSE STRUCTURE
iv
ABOUT THIS BOOK
vi
QUALIFICATION AND ASSESSMENT OVERVIEW
viii
EXTRA ONLINE CONTENT
x
Y 1 BINOMIAL DISTRIBUTIONS
1
P 2 POISSON DISTRIBUTIONS
17
3 APPROXIMATIONS
35
CO 4 CONTINUOUS RANDOM VARIABLES
49
REVIEW EXERCISE 1
5 CONTINUOUS UNIFORM DISTRIBUTION
E 6 SAMPLING AND SAMPLING DISTRIBUTIONS L 7 HYPOTHESIS TESTING P REVIEW EXERCISE 2 M EXAM PRACTICE
BINOMIAL CUMULATIVE DISTRIBUTION TABLES
SAPOISSON CUMULATIVE DISTRIBUTION TABLE
83 87 102 112 132 136 139 144
GLOSSARY
145
ANSWERS
147
INDEX
163
iv COURSE STRUCTURE
CHAPTER 1 BINOMIAL
CHAPTER 4 CONTINUOUS
DISTRIBUTIONS
1 RANDOM VARIABLES
49
1.1 THE BINOMIAL DISTRIBUTION
2 4.1 CONTINUOUS RANDOM
1.2 CUMULATIVE PROBABILITIES
6
VARIABLES
50
1.3 MEAN AND VARIANCE OF THE
BINOMIAL DISTRIBUTION
10
CHAPTER REVIEW 1
14
Y CHAPTER 2 POISSON
P DISTRIBUTIONS
17
2.1 THE POISSON DISTRIBUTION
18
2.2 MODELLING WITH THE POISSON
O DISTRIBUTION
21
2.3 ADDING POISSON DISTRIBUTIONS 26
C 2.4 MEAN AND VARIANCE OF A
POISSON DISTRIBUTION
29
CHAPTER REVIEW 2
31
E CHAPTER 3 APPROXIMATIONS 35
L 3.1 USING THE POISSON DISTRIBUTION
TO APPROXIMATE THE BINOMIAL
DISTRIBUTION36
P 3.2 APPROXIMATING A BINOMIAL
DISTRIBUTION
39
3.3 APPROXIMATING A POISSON
M DISTRIBUTION BY A NORMAL
DISTRIBUTION
42
A 3.4 CHOOSING THE APPROPRIATE
APPROXIMATION
44
SCHAPTER REVIEW 3
45
4.2 T HE CUMULATIVE DISTRIBUTION
FUNCTION
56
4.3 M EAN AND VARIANCE OF A
CONTINUOUS DISTRIBUTION
61
4.4 M ODE, MEDIAN, QUARTILES AND
PERCENTILES
67
CHAPTER REVIEW 4
76
REVIEW EXERCISE 1
83
CHAPTER 5 CONTINUOUS
UNIFORM DISTRIBUTION 87
5.1 THE CONTINUOUS UNIFORM
DISTRIBUTION
88
5.2 M ODELLING WITH THE
CONTINUOUS UNIFORM
DISTRIBUTION
95
CHAPTER REVIEW 5
99
COURSE STRUCTURE
v
CHAPTER 6 SAMPLING AND
REVIEW EXERCISE 2
132
SAMPLING DISTRIBUTIONS 102
6.1 POPULATIONS AND SAMPLES 103 EXAM PRACTICE
136
6.2 THE CONCEPT OF A STATISTIC 104
6.3 T HE SAMPLING DISTRIBUTION
OF A STATISTIC
105 BINOMIAL CUMULATIVE
CHAPTER REVIEW 6
109 DISTRIBUTION TABLES
139
Y CHAPTER 7 HYPOTHESIS
POISSON CUMULATIVE
P TESTING
112 DISTRIBUTION TABLE
144
7.1 HYPOTHESIS TESTING
113
O 7.2 FINDING CRITICAL VALUES
115 GLOSSARY
145
7.3 O NE-TAILED TESTS
119
7.4 T WO-TAILED TESTS
121
C 7.5 T ESTING THE MEAN OF
ANSWERS
147
A POISSON DISTRIBUTION
123
7.6 USING APPROXIMATIONS
127 INDEX
163
SAMPLE CHAPTER REVIEW 7
126
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