The Probability Workbook

The

Probability

Workbook

Mary McShane-Vaughn

ASQ Quality Press

Milwaukee, Wisconsin

Also available from ASQ Quality Press:

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Mary McShane-Vaughn

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Root Cause Analysis: Simplified Tools and Techniques, Second Edition

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The Certified Six Sigma Green Belt Handbook, Second Edition

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The Certified Manager of Quality/Organizational Excellence Handbook, Fourth Edition

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The Certified Six Sigma Black Belt Handbook, Third Edition

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The ASQ Auditing Handbook, Fourth Edition

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To request a complimentary catalog of ASQ Quality Press publications, call 800-248-1946, or visit our website at http://www.asq.org/quality-press.

American Society for Quality, Quality Press, Milwaukee 53203

© 2017 by ASQ

All rights reserved. Published 2017

23  22  21  20  19  18  17        5  4  3  2  1

Library of Congress Cataloging-in-Publication Data

Names: McShane-Vaughn, Mary, 1963– | McShane-Vaughn, Mary, 1963– The probability handbook.

Title: The probability workbook / Mary McShane-Vaughn.

Description: Milwaukee, Wisconsin : ASQ Quality Press, 2017. | Includes bibliographical references and index.

Identifiers: LCCN 2017015067 | ISBN 9780873899574

Subjects: LCSH: Probabilities—Problems, exercises, etc.

Classification: LCC QA273.15 .M46 2017 | DDC 519.2—dc23

LC record available at https://lccn.loc.gov/2017015067

    R729.8.A53 2010

    610.28'9—dc22                2009052472

ISBN: 978-0-87389-957-4

No part of this book may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Ray Zielke: Director, Quality Press and Programs

Paul Daniel O’Mara: Managing Editor

Randall L. Benson: Sr. Creative Services Specialist

ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through learning, quality improvement, and knowledge exchange.

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To place orders or to request ASQ membership information, call 800-248-1946. Visit our website at http://www.asq.org/quality-press.

To Caroline, who found her way to us despite long odds.

Table of Contents

Preface

Acknowledgments

Chapter 1   Introduction

Chapter 2   Learning to Count

2.1 Enumeration

2-1 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

2-2 Configurations Birth Order Die with single dot signifies the problem is less challenging.

2-3 Inspection Fan Assemblies Die with single dot signifies the problem is less challenging.

2-4 Games Coin Toss Die with single dot signifies the problem is less challenging.

2-5 Games Coin, Die, and Card Suit Die with two dots signifies the problem is challenging.

2-6 Famous Problems The Lady Tasting Tea Die with single dot signifies the problem is less challenging.

2-7 Baseball World Series Die with two dots signifies the problem is challenging.

2-8 Configurations The Seating Chart Conundrum Die with single dot signifies the problem is less challenging.

2-9 Travel Itineraries Die with two dots signifies the problem is challenging.

2-10 Famous Problems Einstein’s Riddle Die with two dots signifies the problem is challenging.

2.2 Factorials

2-11 Configurations Arranging Symbols Die with single dot signifies the problem is less challenging.

2-12 Configurations Choosing Passwords Die with two dots signifies the problem is challenging.

2-13 Configurations Inspection Die with single dot signifies the problem is less challenging.

2-14 Travel Travelling Salesman Die with single dot signifies the problem is less challenging.

2-15 Configurations Designing Experiments Die with two dots signifies the problem is challenging.

2-16 Theorems Sterling’s Formula Die with single dot signifies the problem is less challenging.

2-17 Ranking Automobiles Die with single dot signifies the problem is less challenging.

2.3 Permutations

2-18 Ranking Divisions Die with single dot signifies the problem is less challenging.

2-19 Configurations Arranging Letters Die with single dot signifies the problem is less challenging.

2-20 Lottery Daily Numbers Game Die with single dot signifies the problem is less challenging.

2-21 Configurations Inspection Die with two dots signifies the problem is challenging.

2.4 Combinations

2-22 Elections School Board Die with single dot signifies the problem is less challenging.

2-23 Inspection Fan Assemblies Die with single dot signifies the problem is less challenging.

2-24 Inspection Packages Die with single dot signifies the problem is less challenging.

2-25 Application Practice Symmetry Die with single dot signifies the problem is less challenging.

2-26 Application Practice Symmetry Die with two dots signifies the problem is challenging.

2-27 Lottery Daily Numbers Game Die with single dot signifies the problem is less challenging.

2-28 Famous Problems Pascal’s Triangle Die with single dot signifies the problem is less challenging.

2-29 Configurations Pizza Toppings Die with two dots signifies the problem is challenging.

2.5 More Problems

2-30 Travel Travelling Salesman Die with single dot signifies the problem is less challenging.

2-31 Application Practice Combinations and Permutations Die with single dot signifies the problem is less challenging.

2-32 Configuration License Plates Die with single dot signifies the problem is less challenging.

2-33 Configurations License Plates Die with single dot signifies the problem is less challenging.

2-34 Configurations Telephone Numbers Die with single dot signifies the problem is less challenging.

2-35 Configurations Arranging Letters Die with single dot signifies the problem is less challenging.

2-36 Configurations Arranging Letters Die with single dot signifies the problem is less challenging.

2-37 Travel Road Trip Die with two dots signifies the problem is challenging.

2-38 Healthcare Blood Types Die with two dots signifies the problem is challenging.

2-39 Lottery State Lottery Die with single dot signifies the problem is less challenging.

2-40 Lottery Pick 5 Die with single dot signifies the problem is less challenging.

2-41 Configurations Birth Order Die with two dots signifies the problem is challenging.

2-42 Configurations Arranging Boxes Die with two dots signifies the problem is challenging.

2-43 Inspection Tensile Test Die with single dot signifies the problem is less challenging.

2-44 Configurations Automobile Die with single dot signifies the problem is less challenging.

2-45 Configurations Birth Order Die with single dot signifies the problem is less challenging.

2-46 Application Practice Symmetry Die with single dot signifies the problem is less challenging.

2-47 Application Practice Symmetry Die with single dot signifies the problem is less challenging.

2-48 Configurations Nucleic Acid Die with single dot signifies the problem is less challenging.

2-49 Configurations Yogurt Shop Die with single dot signifies the problem is less challenging.

2-50 Configurations Choosing a Committee Die with single dot signifies the problem is less challenging.

2-51 Configurations Window Display Die with single dot signifies the problem is less challenging.

2-52 Configurations Lining Up Die with two dots signifies the problem is challenging.

2-53 Application Practice Common Factorials Die with single dot signifies the problem is less challenging.

2-54 Poker Hands Royal Flush Die with single dot signifies the problem is less challenging.

2-55 Poker Hands Two Hearts Die with two dots signifies the problem is challenging.

2-56 Poker Hands One Pair Die with two dots signifies the problem is challenging.

2-57 Poker Hands Two Pair Die with two dots signifies the problem is challenging.

2-58 Poker Hands Four of a Kind Die with two dots signifies the problem is challenging.

Chapter 3    The Rules of the Game

3.1 Types of Data

3-1 Application Practice Data Types Die with two dots signifies the problem is challenging.

3.2 Sampling

3-2 Sampling Methods Die with single dot signifies the problem is less challenging.

3-3 Sampling Pallets Die with single dot signifies the problem is less challenging.

3-4 Sampling U.S. Congress Die with two dots signifies the problem is challenging.

3-5 Sampling Audit Die with single dot signifies the problem is less challenging.

3-6 Sampling The Bootstrap Die with two dots signifies the problem is challenging.

3.3 Graphical Displays of Data

3-7 Graphs Histogram Die with single dot signifies the problem is less challenging.

3-8 Graphs Histogram Die with single dot signifies the problem is less challenging.

3-9 Graphs Histogram Die with single dot signifies the problem is less challenging.

3-10 Graphs Box-and-Whisker Plot Die with single dot signifies the problem is less challenging.

3-11 Graphs Box-and-Whisker Plot Die with single dot signifies the problem is less challenging.

3-12 Graphs Stem-and-Leaf Plot Die with single dot signifies the problem is less challenging.

3-13 Graphs Stem-and-Leaf Plot Die with two dots signifies the problem is challenging.

3-14 Graphs Stem-and-Leaf Plot, Histogram Die with single dot signifies the problem is less challenging.

3-15 Graphs Dot Plot Die with single dot signifies the problem is less challenging.

3.4 Events, Trials, and Outcomes

3-16 Games Coin Toss Die with single dot signifies the problem is less challenging.

3-17 Configurations Birth Order Die with single dot signifies the problem is less challenging.

3-18 Inspection Fan Assemblies Die with single dot signifies the problem is less challenging.

3-19 Games Last Banana Die with two dots signifies the problem is challenging.

3.5 Classical versus Empirical Probability

3-20 Application Practice Classical versus Empirical Probability Die with single dot signifies the problem is less challenging.

3-21 Poker Hands Royal Flush Die with single dot signifies the problem is less challenging.

3-22 Poker Hands Straight Flush Die with two dots signifies the problem is challenging.

3-23 Poker Hands Flush Die with two dots signifies the problem is challenging.

3-24 Poker Hands Three of a Kind

3-25 Simulation Bank Wait Times Die with single dot signifies the problem is less challenging.

3-26 Games Cards Die with single dot signifies the problem is less challenging.

3.6 Unions and Intersections

3-27 Sets Union, Intersection Die with single dot signifies the problem is less challenging.

3-28 Graphs Venn Diagram Die with single dot signifies the problem is less challenging.

3-29 Hospitality and Tourism Venn Diagram Die with two dots signifies the problem is challenging.

3.7 Complement Rule

3-30 Games Die Toss Die with two dots signifies the problem is challenging.

3-31 Inspection Yield Die with single dot signifies the problem is less challenging.

3-32 Poker Hands At Least One Pair

3.8 Independence

3-33 Application Practice Independence Die with single dot signifies the problem is less challenging.

3-34 Application Practice Independence Die with single dot signifies the problem is less challenging.

3-35 Application Practice Independence Die with two dots signifies the problem is challenging.

3-36 Yield Throughput Yield Die with single dot signifies the problem is less challenging.

3.9 Mutually Exclusive Events

3-37 Application Practice Mutually Exclusive Die with two dots signifies the problem is challenging.

3-38 Definition Mutually Exclusive Events Die with two dots signifies the problem is challenging.

3.10 Calculating Odds

3-39 Predictions Horse Racing Die with single dot signifies the problem is less challenging.

3-40 Predictions Weather Die with single dot signifies the problem is less challenging.

3-41 Elections Prediction Die with single dot signifies the problem is less challenging.

3-42 Games Coin, Die, and Card Die with two dots signifies the problem is challenging.

3.11 Conditional Probability

3-43 Inspection Pallets Die with two dots signifies the problem is challenging.

3-44 Healthcare Blood Types Die with two dots signifies the problem is challenging.

3-45 Games Sum of Two Dice Die with two dots signifies the problem is challenging.

3-46 Games Sum of Two Dice Die with two dots signifies the problem is challenging.

3-47 Sampling Socks in a Drawer Die with two dots signifies the problem is challenging.

3-48 Healthcare Incidence of Lung Cancer Die with two dots signifies the problem is challenging.

3-49 Business Venn Diagram Die with two dots signifies the problem is challenging.

3-50 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-51 Lottery Logic Die with two dots signifies the problem is challenging.

3-52 Inspection Acceptance Sampling Die with two dots signifies the problem is challenging.

3-53 p-Value Statistics

3.12 Multiplication Rule

3-54 Inspection Supplier Quality Die with single dot signifies the problem is less challenging.

3-55 Business Human Resources Die with two dots signifies the problem is challenging.

3-56 Certification Testing Die with two dots signifies the problem is challenging.

3-57 Certification Testing Die with two dots signifies the problem is challenging.

3-58 Famous Problems The Lady Tasting Tea

3-59 Baseball World Series Die with two dots signifies the problem is challenging.

3-60 Baseball World Series Die with two dots signifies the problem is challenging.

3-61 Famous Problems The Problem of Points Die with two dots signifies the problem is challenging.

3-62 Famous Problems The Problem of Points Die with two dots signifies the problem is challenging.

3.13 Addition Rule

3-63 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

3-64 Hospitality and Tourism Marketing Die with two dots signifies the problem is challenging.

3-65 Hospitality and Tourism Marketing Die with two dots signifies the problem is challenging.

3.14 Law of Total Probability and Bayes’ Theorem

3-66 Inspection Glass Panels Die with two dots signifies the problem is challenging.

3-67 Healthcare Hospital Admissions Die with two dots signifies the problem is challenging.

3-68 Famous Problems The Strange Three Boxes Die with two dots signifies the problem is challenging.

3-69 Healthcare Diagnostic Tests

3-70 Business Human Resources

3.15 More Problems

3-71 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-72 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-73 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-74 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-75 Lottery Mega Millions Die with two dots signifies the problem is challenging.

3-76 Poker Hands Royal Flush Die with single dot signifies the problem is less challenging.

3-77 Elections Prediction Die with single dot signifies the problem is less challenging.

3-78 Elections Prediction Die with single dot signifies the problem is less challenging.

3-79 Sampling Socks in a Drawer Die with two dots signifies the problem is challenging.

3-80 Sampling Socks in a Drawer Die with two dots signifies the problem is challenging.

3-81 Inspection Parts in a Bin Die with two dots signifies the problem is challenging.

3-82 Inspection Misclassification

3-83 Inspection Weld Integrity Die with two dots signifies the problem is challenging.

3-84 Healthcare Disease Screening

3-85 Healthcare Disease Screening, Continued

3-86 Famous Problems Birthday Problem Die with two dots signifies the problem is challenging.

3-87 Famous Problems Birthday Problem Die with two dots signifies the problem is challenging.

3-88 Famous Problems Birthday Problem Die with two dots signifies the problem is challenging.

3-89 Famous Problems The Monty Hall Problem Die with two dots signifies the problem is challenging.

3-90 Famous Problems The Monty Hall Problem Die with two dots signifies the problem is challenging.

3-91 Famous Problems The Monty Hall Problem Die with two dots signifies the problem is challenging.

3-92 Famous Problems People v. Collins

3-93 Famous Problems Prosecutor’s Fallacy Die with two dots signifies the problem is challenging.

3-94 Famous Problems The Prisoner’s Problem Die with two dots signifies the problem is challenging.

3-95 Famous Problems Simpson’s Paradox Die with two dots signifies the problem is challenging.

Chapter 4    Discrete Probability Distribution Problems

4.1 Probability Concepts for Discrete Random Variables

4-1 Probability Mass Function Definition Die with single dot signifies the problem is less challenging.

4-2 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

4-3 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

4-4 Games Coin Toss Die with single dot signifies the problem is less challenging.

4-5 Games Coin Toss Die with single dot signifies the problem is less challenging.

4-6 Probability Mass Function Definition Die with single dot signifies the problem is less challenging.

4-7 Probability Mass Function Definition Die with single dot signifies the problem is less challenging.

4-8 Games Die and Coin Die with single dot signifies the problem is less challenging.

4-9 Graphs Probability Mass Function Die with single dot signifies the problem is less challenging.

4-10 Famous Problems The Lady Tasting Tea Die with single dot signifies the problem is less challenging.

4-11 Famous Problems Zipf’s Law Die with two dots signifies the problem is challenging.

4-12 Famous Problems Benford’s Law Die with single dot signifies the problem is less challenging.

4-13 Expectation Probability Mass Function Die with single dot signifies the problem is less challenging.

4-14 Expectation Skewness and Kurtosis Die with two dots signifies the problem is challenging.

4-15 Lottery Mega Millions Die with two dots signifies the problem is challenging.

4-16 Expectation Bias and Variance of Estimators Die with single dot signifies the problem is less challenging.

4-17 Expectation Linear Combinations Die with two dots signifies the problem is challenging.

4-18 Graphs Leptokurtic and Platykurtic Die with single dot signifies the problem is less challenging.

4-19 Graphs Kurtosis Die with single dot signifies the problem is less challenging.

4-20 Games Game Theory Die with two dots signifies the problem is challenging.

4-21 Business Bid Pricing Die with two dots signifies the problem is challenging.

4-22 Sampling Composite Samples Die with two dots signifies the problem is challenging.

4-23 Expectation Expected Winnings

4-24 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

4-25 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

4-26 Application Practice Linear Combinations Die with single dot signifies the problem is less challenging.

4-27 Application Practice Linear Combinations Die with single dot signifies the problem is less challenging.

4-28 Business FICO Scores Die with two dots signifies the problem is challenging.

4-29 Theorems Change of Variables Die with single dot signifies the problem is less challenging.

4-30 Theorems Change of Variables Die with two dots signifies the problem is challenging.

4-31 Application Practice Cumulative Probability Die with two dots signifies the problem is challenging.

4.2 The Discrete Uniform Distribution

4-32 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-33 Application Practice Probability Mass Function Die with single dot signifies the problem is less challenging.

4-34 Application Practice Probability Mass Function Die with single dot signifies the problem is less challenging.

4-35 Expectation Discrete Uniform Die with single dot signifies the problem is less challenging.

4.3 The Binomial Distribution

4-36 Probability Mass Function Definition Die with two dots signifies the problem is challenging.

4-37 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-38 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

4-39 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

4-40 Reliability Stress Test Die with single dot signifies the problem is less challenging.

4-41 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

4-42 Healthcare Emergency Department Die with two dots signifies the problem is challenging.

4-43 Business Bank Loans Die with single dot signifies the problem is less challenging.

4-44 Statistical Process Control Go/No-Go Die with two dots signifies the problem is challenging.

4-45 Statistical Process Control Go/No-Go Die with two dots signifies the problem is challenging.

4-46 Statistical Process Control Electrical Switches Die with two dots signifies the problem is challenging.

4-47 p-Value Stress Genes Die with two dots signifies the problem is challenging.

4-48 Famous Problems The Problem of Points Die with two dots signifies the problem is challenging.

4-49 Famous Problems The Lady Tasting Tea Die with two dots signifies the problem is challenging.

4-50 Simulation Generating Binomial Observations Die with two dots signifies the problem is challenging.

4-51 Statistical Process Control Deming’s Red Bead Experiment Die with two dots signifies the problem is challenging.

4-52 Simulation Project Deming’s Red Bead Experiment Part 1 Die with two dots signifies the problem is challenging.

4-53 Simulation Project Deming’s Red Bead Experiment Part 2 Die with single dot signifies the problem is less challenging.

4-54 Simulation Project Deming’s Red Bead Experiment Part 3 Die with two dots signifies the problem is challenging.

4.4 The Multinomial Distribution

4-55 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-56 Inspection Motors Die with single dot signifies the problem is less challenging.

4-57 Inspection Candy Colors Die with two dots signifies the problem is challenging.

4-58 Elections Prediction Die with two dots signifies the problem is challenging.

4-59 Hospitality and Tourism Airline Seats Die with single dot signifies the problem is less challenging.

4-60 Inspection Incoming Material

4-61 Academia Engineering Majors Die with single dot signifies the problem is less challenging.

4-62 Sampling The Bootstrap

4-63 Sampling The Bootstrap Die with two dots signifies the problem is challenging.

4.5 The Hypergeometric Distribution

4-64 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-65 Probability Mass Function Domain Die with two dots signifies the problem is challenging.

4-66 Probability Mass Function Domain Die with two dots signifies the problem is challenging.

4-67 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

4-68 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

4-69 Application Practice Egg Problem Die with two dots signifies the problem is challenging.

4-70 Games Cards Die with two dots signifies the problem is challenging.

4-71 Inspection Acceptance Sampling Die with single dot signifies the problem is less challenging.

4-72 Healthcare Blood Types Die with single dot signifies the problem is less challenging.

4-73 Approximation Binomial—Hypergeometric Die with two dots signifies the problem is challenging.

4-74 Approximation Binomial—Hypergeometric Die with two dots signifies the problem is challenging.

4-75 Inspection Acceptance Sampling Die with two dots signifies the problem is challenging.

4-76 Inspection Acceptance Sampling

4.6 The Geometric and Negative Binomial Distributions

4-77 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-78 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

4-79 Sampling Inspection Die with single dot signifies the problem is less challenging.

4-80 Inspection Fan Assemblies Die with single dot signifies the problem is less challenging.

4-81 Games Dice and Steps Die with single dot signifies the problem is less challenging.

4-82 Application Practice Conditional Probability Die with two dots signifies the problem is challenging.

4-83 Famous Problems The Gambler’s Fallacy Die with two dots signifies the problem is challenging.

4-84 Famous Problems The Gambler’s Fallacy Die with two dots signifies the problem is challenging.

4-85 Memoryless Property Geometric Distribution Die with two dots signifies the problem is challenging.

4-86 Statistical Process Control Average Run Length Die with single dot signifies the problem is less challenging.

4-87 Application Practice Cumulative Probability Die with single dot signifies the problem is less challenging.

4-88 Simulation Generating Geometric Random Variables Die with two dots signifies the problem is challenging.

4-89 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-90 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

4-91 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

4-92 Application Practice Probability of rth Success Die with two dots signifies the problem is challenging.

4-93 Application Practice Conditional Probability Die with two dots signifies the problem is challenging.

4-94 Simulation Generating Pascal Observations Die with two dots signifies the problem is challenging.

4-95 Famous Problems The Lady Tasting Tea Die with single dot signifies the problem is less challenging.

4-96 Famous Problems The Problem of Points Die with two dots signifies the problem is challenging.

4.7 The Poisson Distribution

4-97 Probability Mass Function Formula Die with single dot signifies the problem is less challenging.

4-98 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

4-99 Expectation Tollgate Die with single dot signifies the problem is less challenging.

4-100 Expectation Paint Defects Die with single dot signifies the problem is less challenging.

4-101 Hospitality and Tourism Safari Die with two dots signifies the problem is challenging.

4-102 Business Banking Die with single dot signifies the problem is less challenging.

4-103 Approximation Poisson—Binomial Die with two dots signifies the problem is challenging.

4-104 Approximation Poisson—Binomial Die with two dots signifies the problem is challenging.

4-105 Approximation Poisson—Binomial Die with two dots signifies the problem is challenging.

4-106 Approximation Throughput Yield Die with two dots signifies the problem is challenging.

4-107 Simulation Convolution Method Die with two dots signifies the problem is challenging.

4-108 Simulation Monte Carlo Die with two dots signifies the problem is challenging.

4-109 Business Customer Demand Die with two dots signifies the problem is challenging.

4-110 Business Customer Demand Die with two dots signifies the problem is challenging.

4-111 Statistical Process Control Tracking Defects Die with two dots signifies the problem is challenging.

4-112 Statistical Process Control Tracking Defects Die with two dots signifies the problem is challenging.

4-113 Statistical Process Control c-Chart Die with two dots signifies the problem is challenging.

4.8 More Problems

4-114 Probability Mass Function Definition Die with single dot signifies the problem is less challenging.

4-115 Probability Mass Function Definition Die with single dot signifies the problem is less challenging.

4-116 Application Practice Discrete Distributions Die with two dots signifies the problem is challenging.

4-117 Inspection Acceptance Sampling Die with single dot signifies the problem is less challenging.

4-118 Inspection Acceptance Sampling Die with two dots signifies the problem is challenging.

4-119 Inspection Circuit Boards Die with two dots signifies the problem is challenging.

4-120 Application Practice Probability Mass Function Die with single dot signifies the problem is less challenging.

4-121 Approximations Throughput Yield Die with single dot signifies the problem is less challenging.

4-122 Inspection Incoming Material Die with two dots signifies the problem is challenging.

4-123 Academia Gender Bias Die with two dots signifies the problem is challenging.

4-124 Academia Gender Bias, Continued Die with two dots signifies the problem is challenging.

4-125 Application Practice Variance Die with single dot signifies the problem is less challenging.

Chapter 5    Continuous Probability Distributions

5.1 Probability Concepts for Continuous Random Variables

5-1 Probability Density Function Definition Die with single dot signifies the problem is less challenging.

5-2 Graphs Cumulative Probability Die with single dot signifies the problem is less challenging.

5.2 Useful Probability Theorems

5-3 Theorems Markov’s Inequality Die with single dot signifies the problem is less challenging.

5-4 Theorems Markov’s Inequality Die with two dots signifies the problem is challenging.

5-5 Theorems Chebyshev’s Inequality Die with single dot signifies the problem is less challenging.

5-6 Theorems Chebyshev’s Inequality Die with two dots signifies the problem is challenging.

5-7 Theorems Chebyshev’s Inequality Die with two dots signifies the problem is challenging.

5-8 Theorems Chebyshev’s Inequality Die with two dots signifies the problem is challenging.

5.3 The Uniform Distribution

5-9 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-10 Graphs Probability Density Function Die with single dot signifies the problem is less challenging.

5-11 Graphs Probability Density Function Die with two dots signifies the problem is challenging.

5-12 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-13 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-14 Simulation Bernoulli Observations Die with single dot signifies the problem is less challenging.

5-15 Simulation Generating Uniform Observations Die with two dots signifies the problem is challenging.

5-16 Simulation Generating Uniform Observations Die with two dots signifies the problem is challenging.

5.4 The Triangular Distribution

5-17 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-18 Graphs Probability Density Function Die with two dots signifies the problem is challenging.

5-19 Graphs Cumulative Density Function Die with two dots signifies the problem is challenging.

5-20 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-21 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5.5 The Normal Distribution

5-22 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-23 Graphs Matching Distributions Die with single dot signifies the problem is less challenging.

5-24 Proof Unbiased Estimators Die with two dots signifies the problem is challenging.

5-25 Proof Unbiased Estimators

5-26 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-27 Graphs Normal Probability Plots Die with two dots signifies the problem is challenging.

5-28 Theorems Central Limit Theorem Die with single dot signifies the problem is less challenging.

5-29 Theorems Central Limit Theorem

5-30 Theorems Central Limit Theorem Die with two dots signifies the problem is challenging.

5-31 Academia ACT Scores Die with two dots signifies the problem is challenging.

5-32 Manufacturing Linear Combinations

5-33 Manufacturing Fill Weights Die with two dots signifies the problem is challenging.

5-34 Parameters Heights of Men

5-35 Approximation Appropriateness Die with two dots signifies the problem is challenging.

5-36 Approximation Normal—Binomial Die with two dots signifies the problem is challenging.

5-37 Approximation Normal—Poisson Die with two dots signifies the problem is challenging.

5-38 Approximation Normal—Gamma Die with two dots signifies the problem is challenging.

5-39 Simulation Box-Muller Method Die with two dots signifies the problem is challenging.

5-40 Mean Shift Six Sigma Die with two dots signifies the problem is challenging.

5-41 Statistical Process Control Type I and Type II Errors

5-42 Statistical Process Control X– and R Chart Die with two dots signifies the problem is challenging.

5-43 Statistical Process Control X– and s Chart Die with two dots signifies the problem is challenging.

5-44 Statistical Process Control Western Electric Rules

5-45 Statistical Process Control Western Electric Rules Die with two dots signifies the problem is challenging.

5-46 Statistical Process Control Western Electric Rules Die with two dots signifies the problem is challenging.

5.6 The Standard Normal Distribution

5-47 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-48 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-49 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-50 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-51 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-52 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-53 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-54 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-55 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-56 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-57 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-58 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-59 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-60 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-61 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-62 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-63 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-64 Application Practice Probability Statement Die with two dots signifies the problem is challenging.

5-65 Manufacturing Quality Metrics Die with single dot signifies the problem is less challenging.

5-66 Mean Shift Supplier Quality Die with single dot signifies the problem is less challenging.

5-67 Sampling Margin of Error Die with two dots signifies the problem is challenging.

5-68 Mean Shift Yield Die with two dots signifies the problem is challenging.

5-69 Metrics Height and IQ Die with two dots signifies the problem is challenging.

5-70 Manufacturing Specifications Die with two dots signifies the problem is challenging.

5-71 Manufacturing Mean Shift Die with single dot signifies the problem is less challenging.

5.7 The Student’s t Distribution

5-72 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-73 Probability Density Function Formula

5-74 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-75 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-76 Expectation Mean and Variance Die with two dots signifies the problem is challenging.

5-77 Probability Density Function Variance and Degrees of Freedom Die with two dots signifies the problem is challenging.

5-78 Application Practice Using the Student’s t Table Die with single dot signifies the problem is less challenging.

5-79 Guinness Head Height Die with two dots signifies the problem is challenging.

5-80 Automotive Miles per Gallon Die with single dot signifies the problem is less challenging.

5.8 The Gamma Distribution

5-81 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-82 Application Practice Gamma Function Die with two dots signifies the problem is challenging.

5-83 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-84 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-85 Simulation Choosing Parameters Die with two dots signifies the problem is challenging.

5-86 Simulation Wait Time

5-87 Shipments Time to Delivery Die with two dots signifies the problem is challenging.

5-88 Reliability Mean Time between Failures Die with single dot signifies the problem is less challenging.

5.9 The Chi-square Distribution

5-89 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-90 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-91 Theorems Cochran’s Theorem Die with single dot signifies the problem is less challenging.

5-92 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-93 Healthcare Chi-Square Test of Independence

5-94 Famous Problems Benford’s Law

5-95 Application Practice Test of Variance Die with single dot signifies the problem is less challenging.

5.10 The Exponential Distribution

5-96 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-97 Cumulative Density Function Formula Die with single dot signifies the problem is less challenging.

5-98 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-99 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-100 Memoryless Property Exponential Distribution Die with two dots signifies the problem is challenging.

5-101 Proof Memoryless Property Die with two dots signifies the problem is challenging.

5-102 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-103 Reliability Probability of Failure Die with two dots signifies the problem is challenging.

5-104 Reliability Engine Assembly Die with single dot signifies the problem is less challenging.

5-105 Reliability Reliability at Time t Die with single dot signifies the problem is less challenging.

5-106 Reliability Mean Time to Failure Die with single dot signifies the problem is less challenging.

5-107 Reliability Warranty Costs

5-108 Reliability Warranty Period Die with two dots signifies the problem is challenging.

5-109 Reliability Mean Time to Failure of an Assembly Die with two dots signifies the problem is challenging.

5-110 Reliability System Failure Die with two dots signifies the problem is challenging.

5-111 Reliability Series System Die with two dots signifies the problem is challenging.

5-112 Reliability Parallel System

5-113 Reliability Hazard Function Die with two dots signifies the problem is challenging.

5-114 Probability Density Function Poisson–Exponential Connection Die with two dots signifies the problem is challenging.

5-115 Simulation Wait Time Die with single dot signifies the problem is less challenging.

5-116 Simulation Generating Exponential Observations Die with two dots signifies the problem is challenging.

5.11 The Weibull Distribution

5-117 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-118 Cumulative Density Function Formula Die with single dot signifies the problem is less challenging.

5-119 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-120 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-121 Expectation Mean and Variance Die with two dots signifies the problem is challenging.

5-122 Reliability Function Die with single dot signifies the problem is less challenging.

5-123 Reliability Mechanical Switch Die with single dot signifies the problem is less challenging.

5-124 Reliability Failure Probability Die with single dot signifies the problem is less challenging.

5-125 Reliability Hazard Function Die with two dots signifies the problem is challenging.

5-126 Reliability Hazard Function Die with two dots signifies the problem is challenging.

5-127 Reliability Hazard Function Die with two dots signifies the problem is challenging.

5-128 Reliability Proof Die with single dot signifies the problem is less challenging.

5-129 Simulation Generating Weibull Observations Die with two dots signifies the problem is challenging.

5.12 The F-Distribution

5-130 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-131 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-132 Probability Density Function Formula

5-133 Probability Density Function Formula Die with two dots signifies the problem is challenging.

5-134 Probability Density Function Formula

5-135 Probability Density Function Formula

5-136 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-137 Application Practice F-Table Die with two dots signifies the problem is challenging.

5-138 Application Practice F Values Die with two dots signifies the problem is challenging.

5-139 Application Practice Testing Variances Die with two dots signifies the problem is challenging.

5.13 The Beta Distribution

5-140 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-141 Application Practice Beta Function Die with two dots signifies the problem is challenging.

5-142 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-143 Probability Density Function Analyze Die with two dots signifies the problem is challenging.

5-144 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-145 Application Practice Fraction Defective Die with single dot signifies the problem is less challenging.

5-146 Yield Welded Assembly Die with two dots signifies the problem is challenging.

5-147 Application Practice Process Time Die with two dots signifies the problem is challenging.

5-148 Probability Density Function Poisson–Beta Connection Die with two dots signifies the problem is challenging.

5.14 The Lognormal Distribution

5-149 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-150 Graphs Matching Distributions Die with two dots signifies the problem is challenging.

5-151 Expectation Mean and Variance Die with single dot signifies the problem is less challenging.

5-152 Application Practice Probability Statement Die with single dot signifies the problem is less challenging.

5-153 Probability Density Function Lognormal and Normal Die with two dots signifies the problem is challenging.

5-154 Manufacturing Quality Index Die with two dots signifies the problem is challenging.

5.15 The Cauchy Distribution

5-155 Probability Density Function Formula Die with single dot signifies the problem is less challenging.

5-156 Proof Cauchy and Student’s t Die with two dots signifies the problem is challenging.

Appendix A: Problem Solutions

Solutions for Chapter 2

2-1 Games Sum of Two Dice Die with single dot signifies the problem is less challenging.

2-2 Configurations Birth Order Die with single dot signifies the problem is less challenging.

2-3 Inspection Fan Assemblies Die with single dot signifies the problem is less challenging.

2-4 Games Coin Toss Die with single dot signifies the problem is less challenging.

2-5 Games Coin, Die, and Card Suit Die with two dots signifies the problem is challenging.

2-6 Famous Problems The Lady Tasting Tea Die with single dot signifies the problem is less challenging.

2-7 Baseball World Series Die with two dots signifies the problem is challenging.

2-8 Configurations The Seating Chart Conundrum Die with single dot signifies the problem is less challenging.

2-9 Travel Itineraries Die with two dots signifies the problem is challenging.

2-10 Famous Problems Einstein’s Riddle Die with two dots signifies the problem is challenging.

2-11 Configurations Arranging Symbols Die with single dot signifies the problem is less challenging.

2-12 Configurations Choosing Passwords Die with two dots signifies the problem is challenging.

2-13 Configurations Inspection Die with single dot signifies the problem is less challenging.

2-14 Travel Traveling Salesman Die with single dot signifies the problem is less challenging.

2-15 Configurations Designing Experiments Die with two dots signifies the problem is challenging.

2-16 Theorems Sterling’s Formula Die with single dot signifies the problem is less challenging.

2-17 Ranking Automobiles Die with single dot signifies the problem is less challenging.

2-18 Ranking Divisions Die with single dot signifies the problem is less challenging.

2-19 Configurations Arranging Letters Die with single dot signifies the problem is less challenging.

2-20 Lottery Daily Numbers Game Die with single dot signifies the problem is less challenging.

2-21 Configurations Inspection Die with two dots signifies the problem is challenging.