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

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ISBN 978 1 292245 17 1

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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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