MATH 132 Problem Solving: Algebra, Probability, and Statistics

MATH 132 Problem Solving: Algebra, Probability,

and Statistics

FALL 2018

Typeset: August 11, 2018

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MATH 132 ? Problem Solving: Algebra, Probability, and Statistics Lecture notes version 1.3 (Fall 2018)

Copyright (c) 2009-2018 Carolyn Abbott, Claire Blackman, Anne Candioto, Benjamin Ellison, Allison Gordon, Edward Hanson, Diane Holcomb, Noah Kieserman, Oh Hoon Kwon, Christine Lien, Daniel McGinn, Balazs Strenner, Elizabeth Skubak Wolf, Quinton Westrich Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.0 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license can be found at .

Contents

1 Probability

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1.1 Flipping Coins: An Introduction to Probability . . . . . . . . . . . . . . . . . . . . 5

1.2 Sample Spaces and Equally Likely Outcomes . . . . . . . . . . . . . . . . . . . . . 9

1.3 Modeling Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 More Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.5 Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.6 Using Models in Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Statistics

25

2.1 Measures of Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Measures of Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3 Histograms, Stem-and-Leaf Plots, & Box Plots . . . . . . . . . . . . . . . . . . . 31

2.4 Scatterplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5 Misleading Graphs & Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Algebra

43

3.1 Patterns and Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2 Patterns and Rules II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.3 Linear Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.4 Proportional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.5 Non-linear Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6 Ratio and Proportions Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

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CONTENTS

Chapter 1

Probability

1.1 Flipping Coins: An Introduction to Probability

Consider playing a game where there are two teams, the Brewers and the Cubs. You flip two coins at the same time; if the faces that come up match (i.e. both heads or both tails), then the Brewers get a point. If the faces are different, then the Cubs get a point. I'll come around with coins. Don't actually flip any of them until you get to the second question.

1. Suppose you were to flip the coins ten times. Which team do you think would have the most points? Make an exact prediction for the score (like 10-0, or 7-3). For what reasons did you come up with that prediction?

2. Now actually flip the coins ten times and keep score. Did the outcome match your prediction? Do you think this is a coincidence? Do you think your prediction was a good one? a bad one? and why? Do these results make you want to change your prediction? If so, what is your prediction now?

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