Table Of Content

2222222 Anoka-Hennepin ooo 2 7777555 Probability and Statistics 33333 66666666666 999 99999999 44444444444 2222 2 666666 333 44444444444 ooooo 999999 identify your path STEP 66666666666666666666666666666666 111 5555555 99999999999999 444444444444444 oooooooo 666666666 222222222 333333333333 4444444444444444444444444444444444444444444444444444444444444444444 3333333 777777 88888888 Fourth Edition 55550000000000000000007777777 99999 99999999999999999955555555555 11111 999999999999999999999 8888 Haney Johnson 222222222222222 55555555 77 111 To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook mate- rials for the K-12 market both in the U.S. and worldwide. 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Printed: July 24, 2013 Authors Ms. Heather Haney, Mr. Ernest Johnson Contributors Mr. Bruce DeWitt, Mr. Michael Engelhaupt, Ms. Anne Roehrich, Mr. Tom Skoglund, Mr. Matthew Henderson Editors Ms. Katie Bruck, Ms. Elizabeth Dorsing, Ms. Wendy Durant, Mr. Charles Nowariak, Ms. Julie Rydberg, Ms. Meghann Witchger i www.ck12.org Contents Foreword iv Preface v 1 Counting Methods 1 1.1 Sample Spaces, Events, and Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fundamental Counting Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Mixed Combinations and Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6 Chapter 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Calculating Probabilities 27 2.1 Calculating Basic Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Compound and Independent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3 Mutually Exclusive Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 Tree Diagrams and Probability Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.5 Conditional Probabilities and 2-Way Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.6 Chapter 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3 Expected Values & Simulation 77 3.1 Probability Models & Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.2 Applied Expected Value Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 Simulation and Experimental Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4 Chapter 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4 Data Collection 104 4.1 DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.2 Sample Survey and Census . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.3 Random Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 www.ck12.org ii 4.4 Statistical Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.5 Experiments and Observational Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.6 Chapter 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5 Analyzing Univariate Data 155 5.1 Categorical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.2 Time Plots & Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.3 Numerical Data: Dot Plots & Stem Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 5.4 Numerical Data: Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 5.5 Numerical Data: Box Plots & Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 5.6 Numerical Data: Comparing Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 5.7 Chapter 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6 Analyzing Bivariate Data 247 6.1 Displaying Bivariate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 6.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 6.3 Least-Squares Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 6.4 More Least-Squares Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.5 Chapter 6 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7 The Normal Distribution 296 7.1 Introduction to the Normal Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 7.2 Z-Scores, Percentiles, and Normal CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 7.3 Inverse Normal Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 7.4 Chapter 7 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 8 Appendices 325 8.1 Appendix A - Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 8.2 Appendix B - Glossary and Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 8.3 Appendix C - Calculator Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 iii www.ck12.org Foreword Anoka-Hennepin Schools is fortunate to have many experienced math teachers contribute to this project. These primary authors, along with the editing team, worked tirelessly during the summer to complete the formidable task of completing the third edition of the Flexbook in 60 days. Meet the Authors Heather Haney has taught high school mathematics for 20 years and currently teaches at Coon Rapids High School in Coon Rapid, MN. She received her BS in Mathematics from St. Cloud State, MN (1991) and her M. Ed. in Curriculum and Instruction from Texas Wesleyan University (2003). Heather teaches AP and non AP Probability and Statistics. Ernest Johnson currently teaches mathematics at Andover High School in Andover, MN. He has taught mathematics for 20 years teaching courses varying from Algebra, to Statistics, to AP Calculus. Ernest graduated from the University of Minnesota in 1992 with a B.S. in Mathematics and received a M.Ed. in Instructional Systems and Technology in 1998 from the University of Minnesota. About the Videos Helpful video links have been added to the online version of the Flexbook by Matthew Henderson. Matt teaches at Andover HS in Andover MN. He received a B.S. Secondary Mathematics Education. North- western College. St. Paul, MN (1996) and his M.Ed. Curriculum & Instruction: Instructional Systems & Technology at the University of Minnesota (2002). Matt teaches AP and non AP Probability and Statistics both online and offline. Figure 1.1 When you see this image it indicates that a video tutorial is available and you should access the textbook online to view the videos. If you do not have internet or have a slow connection, talk to your teacher about getting a DVD with the videos. www.ck12.org iv Preface About the Book Anoka-HennepinSchoolsisthrilledtoreleasethethirdpublicationofitsveryownProbabilityandStatistics textbook. Anoka-HennepinProbabilityandStatistics (ThirdEdition)representstheworkofalargeteamof dedicated writers and editors who have produced a truly unique and flexible ‘‘ebook.” Available in multiple electronic formats, the content demonstrates 21st century math learning at is finest. Students can access the book from a CD-ROM, DVD, flash drive, or mobile device like the Kindle or ipod. Access is also available through the web anywhere and anytime in multiple formats. Technology While paper copies are available for classroom use, the ebook is interactive and includes web site links, simulations, videos, and real world statistical examples. Students can access the textbook through the district Learning Management Site Moodle where large amounts of supplemental and enrichment content can also be found. The ebook incorporates the use of the TI 83/84 graphing calculators and students work with spread- sheet software to display and manipulate statistical data. Additional content is available through Kahn Academy, which offers individualized problem activities with instructional videos. Find the ebook @ Http://moodle.anoka.k12.mn.us. An epub is available for electronic download from Ck12.org. Navigate there with your IOS device, search for Anoka Hennepin and then download the epub version. Coverage This foundational course covers the Minnesota Data, Analysis, and Probability benchmarks. The course also meets Anoka-Hennepin math graduation requirements. Goals From the Minnesota Twins to the weather forecast statistics are used everywhere in our lives. Anoka- Hennepin Probability and Statistics demonstrates the connection between statistics and our real world. Students- Read and immerse yourself in this interactive textbook. Challenge yourself to dig deeper into the content or find solutions to your questions online. This textbook is alive and responsive to your needs. Give feedback to your teacher for incorporation into later revisions. Your input is valued going forward. Thank you. v www.ck12.org Chapter 1 Counting Methods 1.1 Sample Spaces, Events, and Outcomes Learning Objectives • Determine the sample space for a given event or series of events • Produce an organized list of outcomes within a sample space A sample space is a list of all the possible outcomes that may occur. What might happen when you flip a coin? You will either get heads or tails. What will happen when you roll a single die? You will either get a 1, 2, 3, 4, 5, or 6. The sample space for flipping a coin is S={heads, tails}. The sample space for rolling a die is S={1,2,3,4,5,6} Onacoinflip, therearetwooutcomes, headsandtails. Therearesixdifferentoutcomeswhenconsidering the event of rolling a single die. Example 1 Suppose you roll two dice. Build a 6 by 6 grid to show the different outcomes that might happen when you add the two dice together. a) What is the sample space for the different sums that you might get? b) What is the event for this situation? c) Based on your grid, which outcome occurs most often? 1 www.ck12.org Solution a) The sample space is S={2,3,4,5,6,7,8,9,10,11,12}. b) The event is the rolling of the two dice. c) Notice that a total of 7 can occur 6 different ways. A total of 7 is the most likely outcome. Example 2 A child orders breakfast at a restaurant. The restaurant has two choices of drinks: milk and orange juice. The restaurant also has three choices of meat: sausage, ham, and bacon. Suppose the child orders one drink and one type of meat. a) Give the sample space that shows all the different outcomes for what the child might order. b) How many different outcomes are possible? Solution a) For the drinks, use M=Milk and O=Orange Juice. For the meat, use S=Sausage, H=Ham, and B=Bacon. The child might order MS, MH, MB, OS, OH, or OB. The sample space is S={MS, MH, MB, OS, OH, OB}. This list can also be generated using a simple grid as shown on the top of the next page. www.ck12.org 2