Estadística

Applied Statistics and Probability for Engineers
Third Edition

Douglas C. Montgomery
Arizona State University

George C. Runger
Arizona State University

John Wiley & Sons, Inc.

ACQUISITIONS EDITOR Wayne Anderson ASSISTANT EDITOR Jenny Welter MARKETING MANAGER Katherine Hepburn SENIOR PRODUCTION EDITOR Norine M. Pigliucci DESIGN DIRECTOR Maddy Lesure ILLUSTRATION EDITOR Gene AielloPRODUCTION MANAGEMENT SERVICES TechBooks

This book was set in Times Roman by TechBooks and printed and bound by Donnelley/Willard. The cover was printed by Phoenix Color Corp.

This book is printed on acid-free paper.

Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by anymeans, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978)750-4470. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM. To order books please call 1(800)-225-5945.

Library of Congress Cataloging-in-Publication Data Montgomery, Douglas C. Applied statistics and probability for engineers /Douglas C. Montgomery, George C. Runger.—3rd ed. p. cm. Includes bibliographical references and index. ISBN 0-471-20454-4 (acid-free paper) 1. Statistics. 2. Probabilities. I. Runger, George C. II. Title. QA276.12.M645 2002 519.5—dc21 2002016765

Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1

Preface

The purpose of this Student Solutions Manual is to provide you withadditional help in understanding the problem-solving processes presented in Applied Statistics and Probability for Engineers. The Applied Statistics text includes a section entitled “Answers to Selected Exercises,” which contains the final answers to most odd-numbered exercises in the book. Within the text, problems with an answer available are indicated by the exercise number enclosed in a box. ThisStudent Solutions Manual provides complete worked-out solutions to a subset of the problems included in the “Answers to Selected Exercises.” If you are having difficulty reaching the final answer provided in the text, the complete solution will help you determine the correct way to solve the problem. Those problems with a complete solution available are indicated in the “Answers to Selected Exercises,”again by a box around the exercise number. The complete solutions to this subset of problems may also be accessed by going directly to this Student Solutions Manual.

Chapter 2 Selected Problem Solutions Section 2-2 2-43. 3 digits between 0 and 9, so the probability of any three numbers is 1/(10*10*10); 3 letters A to Z, so the probability of any three numbers is 1/(26*26*26); The probabilityyour license plate -8 is chosen is then (1/103)*(1/263) = 5.7 x 10

Section 2-3 2-49. a) P(A') = 1- P(A) = 0.7 b) P ( A ∪ B ) = P(A) + P(B) - P( A ∩ B ) = 0.3+0.2 - 0.1 = 0.4 c) P( A ′ ∩ B ) + P( A ∩ B ) = P(B). Therefore, P( A ′ ∩ B ) = 0.2 - 0.1 = 0.1 d) P(A) = P( A ∩ B ) + P( A ∩ B ′ ). Therefore, P( A ∩ B ′ ) = 0.3 - 0.1 = 0.2 e) P(( A ∪ B )') = 1 - P( A ∪ B ) = 1 - 0.4 = 0.6 f) P( A ′ ∪ B )= P(A') + P(B) - P( A ′ ∩ B ) = 0.7 + 0.2 - 0.1 = 0.8

Section 2-4 2-61. Need data from example a) P(A) = 0.05 + 0.10 = 0.15 P( A ∩ B) 0.04 + 0.07 b) P(A|B) = = = 0.153 P( B ) 0.72 c) P(B) = 0.72 P( A ∩ B) 0.04 + 0.07 d) P(B|A) = = = 0.733 P( B ) 0.15 e) P(A ∩ B) = 0.04 +0.07 = 0.11 f) P(A ∪ B) = 0.15 + 0.72 – 0.11 = 0.76 2-67. a) P(gas leak) = (55 + 32)/107 = 0.813 b) P(electric failure|gas...