PEARSON EDEXCEL INTERNATIONAL A LEVEL STATISTICS 2 Student Book Series Editors: Joe Skrakowski and Harry Smith COPY Authors: Greg Attwood, Tom Begley, Ian Bettison, Alan Clegg, Martin Crozier, Gill Dyer, Jane Dyer, Keith Gallick, Susan Hooker, Michael Jennings, John Kinoulty, Mohammed Ladak, Guilherme Frederico Lima, Jean Littlewood, Bronwen Moran, James Nicholson, Su Nicholson, Laurence Pateman, Keith Pledger, Joe Skrakowski, Harry Smith SAMPLE Published by Pearson Education Limited, 80 Strand, London, WC2R 0RL. Endorsement Statement In order to ensure that this resource offers high-quality support for the associated www.pearsonglobalschools.com Pearson qualification, it has been through a review process by the awarding body. This process confirms that this resource fully covers the teaching and learning Copies of official specifications for all Pearson qualifications may be found on the content of the specification or part of a specification at which it is aimed. It also website: https://qualifications.pearson.com confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in addition to preparation for Text © Pearson Education Limited 2019 assessment. Edited by Eric Pradel Typeset by Tech-Set Ltd, Gateshead, UK Endorsement does not cover any guidance on assessment activities or processes Original illustrations © Pearson Education Limited 2019 (e.g. practice questions or advice on how to answer assessment questions) Illustrated by © Tech-Set Ltd, Gateshead, UK included in the resource, nor does it prescribe any particular approach to the Cover design by © Pearson Education Limited 2019 teaching or delivery of a related course. The rights of Greg Attwood, Tom Begley, Ian Bettison, Alan Clegg, Martin Crozier, While the publishers have made every attempt to ensure that advice on the Gill Dyer, Jane Dyer, Keith Gallick, Susan Hooker, Michael Jennings, John Kinoulty, qualification and its assessment is accurate, the official specification and Mohammed Ladak, Guilherme Frederico Lima, Jean Littlewood, Bronwen Moran, associated assessment guidance materials are the only authoritative source of James Nicholson, Su Nicholson, Laurence Pateman, Keith Pledger, Joe Skrakowski information and should always be referred to for definitive guidance. and Harry Smith to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Pearson examiners have not contributed to any sections in this resource relevant to examination papers for which they have responsibility. First published 2019 Examiners will not use endorsed resources as a source of material for any 22 21 20 19 assessment set by Pearson. Endorsement of a resource does not mean that the 10 9 8 7 6 5 4 3 2 1 resource is required to achieve this Pearson qualification, nor does it mean that it is the only suitable material available to support the qualification, and any resource British Library Cataloguing in Publication Data lists produced by the awarding body shall include this and other appropriate A catalogue record for this book is available from the British Library resources. ISBN 978 1 292245 17 1 Copyright notice All rights reserved. No part of this may be reproduced in any form or by any means (including photocopying or storing it in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) COPY without the written permission of the copyright owner, except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, 5th Floor, Shackleton House, 4 Battlebridge Lane, London, SE1 2HX (www.cla.co.uk). Applications for the copyright owner’s written permission should be addressed to the publisher. Printed in Slovakia by Neografia Picture Credits The authors and publisher would like to thank the following individuals and organisations for permission to reproduce photographs: To be updated: Shutterstock.com: 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: Shutterstock.com: Dmitry Lobanov All other images © Pearson Education Limited 2019 All artwork © Pearson Education Limited 2019 SAMPLE CONTENTS iii COURSE STRUCTURE iv ABOUT THIS BOOK vi QUALIFICATION AND ASSESSMENT OVERVIEW viii EXTRA ONLINE CONTENT x 1 BINOMIAL DISTRIBUTIONS 1 2 POISSON DISTRIBUTIONS 17 3 APPROXIMATIONS 35 4 CONTINUOUS RANDOM VARIABLES 49 REVIEW EXERCISE 1 COPY83 5 CONTINUOUS UNIFORM DISTRIBUTION 87 6 SAMPLING AND SAMPLING DISTRIBUTIONS 102 7 HYPOTHESIS TESTING 112 REVIEW EXERCISE 2 132 EXAM PRACTICE 136 BINOMIAL CUMULATIVE DISTRIBUTION TABLES 139 POISSON CUMULATIVE DISTRIBUTION TABLE 144 GLOSSARSAMPLEY 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 4.2 THE CUMULATIVE DISTRIBUTION BINOMIAL DISTRIBUTION 10 FUNCTION 56 CHAPTER REVIEW 1 14 4.3 MEAN AND VARIANCE OF A CONTINUOUS DISTRIBUTION 61 CHAPTER 2 POISSON 4.4 MODE, MEDIAN, QUARTILES AND PERCENTILES 67 DISTRIBUTIONS 17 CHAPTER REVIEW 4 76 2.1 THE POISSON DISTRIBUTION 18 2.2 MODELLING WITH THE POISSON DISTRIBUTION 21 REVIEW EXERCISE 1 83 2.3 ADDING POISSON DISTRIBUTIONS 26 2.4 MEAN AND VARIANCE OF A CHAPTER 5 CONTINUOUS POISSON DISTRIBUTION 29 COPY UNIFORM DISTRIBUTION 87 CHAPTER REVIEW 2 31 5.1 THE CONTINUOUS UNIFORM DISTRIBUTION 88 CHAPTER 3 APPROXIMATIONS 35 5.2 MODELLING WITH THE 3.1 USING THE POISSON DISTRIBUTION CONTINUOUS UNIFORM TO APPROXIMATE THE BINOMIAL DISTRIBUTION 95 DISTRIBUTION 36 CHAPTER REVIEW 5 99 3.2 APPROXIMATING A BINOMIAL DISTRIBUTION 39 3.3 APPRO XIMATING A POISSON DISTRIBUTION BY A NORMAL DISTRIBUTION 42 3.4 CHOOSING THE APPROPRIATE APPROXIMATION 44 CHAPTERSAMPLE REVIEW 3 45 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 THE SAMPLING DISTRIBUTION OF A STATISTIC 105 BINOMIAL CUMULATIVE CHAPTER REVIEW 6 109 DISTRIBUTION TABLES 139 CHAPTER 7 HYPOTHESIS POISSON CUMULATIVE TESTING 112 DISTRIBUTION TABLE 144 7.1 HYPOTHESIS TESTING 113 7.2 FINDING CRITICAL VALUES 115 GLOSSARY 145 7.3 ONE-TAILED TESTS 119 7.4 TWO-TAILED TESTS 121 7.5 TESTING THE MEAN OF ANSWERS 147 A POISSON DISTRIBUTION 123 COPY 7.6 USING APPROXIMATIONS 127 INDEX 163 CHAPTER REVIEW 7 126 SAMPLE vi ABOUT THIS BOOK ABOUT THIS BOOK The following three themes have been fully integrated throughout the Pearson Edexcel International Advanced Level in Mathematics series, so they can be applied alongside your learning. 1. Mathematical argument, language and proof • Rigorous and consistent approach throughout • Notation boxes explain key mathematical language and symbols 2. Mathematical problem-solving The Mathematical Problem-Solving Cycle • Hundreds of problem-solving questions, fully integrated specify the problem into the main exercises • Problem-solving boxes provide tips and strategies interpret results collect information • Challenge questions provide extra stretch process and 3. Transferable skills represent information • Transferable skills are embedded throughout this book, in the exercises and in some examples • These skills are signposted to show students which skills they are usingCOPY and developing Finding your way around the book Each chapter is mapped to the specification content for easy reference Each chapter starts with a list of Learning objectives The Prior knowledge check helps make sure you are ready to start the chapter The real world applications of the maths you are about to learn SAMPLE are highlighted at the start of the chapter. Glossary terms will be identified by bold blue text on their first appearance. ABOUT THIS BOOK vii Each section begins with explanation and key learning points Transferable skills are signposted where they naturally occur in the exercises and examples Step-by-step worked examples focus on the key types of questions you’ll need to tackle Problem-solving boxes provide hints, Exercises are packed Exercise questions are carefully tips and strategies, and Watch out with exam-style graded so they increase in Exam-style questions boxes highlight areas where students questions to ensure you difficulty and gradually bring often lose marks in their exams are ready for the exams you up to exam standard are flagged with E COPY Problem-solving questions are flagged Each chapter ends with a Chapter review and a Summary of key points with P After every few chapters, a Review exercise helps you consolidate your learning with lots of exam-style questions SAMPLE A full practice paper at the back of the book helps you prepare for the real thing viii QUALIFICATION AND ASSESSMENT OVERVIEW QUALIFICATION AND ASSESSMENT OVERVIEW Qualification and content overview Statistics 2 (S2) is an optional unit in the following qualifications: International Advanced Subsidiary in Further Mathematics International Advanced Level in Mathematics International Advanced Level in Further Mathematics Assessment overview The following table gives an overview of the assessment for this unit. We recommend that you study this information closely to help ensure that you are fully