### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Elementary Probability & Statistics MATH 1530

pellissippi state community college

GPA 3.92

### View Full Document

## 22

## 0

## Popular in Course

## Popular in Mathematics (M)

This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1530 at pellissippi state community college taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/232966/math-1530-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.

## Similar to MATH 1530 at pellissippi state community college

## Popular in Mathematics (M)

## Reviews for Elementary Probability & Statistics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/01/15

3mmquot 4 Overview Pmbab39l39ty D39str39bUt39ons This chapter will deal with the 41 Overview construction of 42 Random Variables probability distributions 43 Binomial Probability Distributions by combining the methods of Chapter 2 44 Mean Variance Standard Deviation With the those f Chapter 3 f r 9 Bin mia39 Distributb Probability Distributions will describe what will probably happen instead of what actually did happen Combining Descriptive Statistics Methods and Probabilities to Form a Theoretical Model of 4 2 Figure 41 BehaVIor x f C I y I a Chapter I a scfsumpe 2 lo Random Va rlables get statistics 5 l2 5 7 describing howt periment and graphs 5 H is upgcfzd to behave t en 5 J get irs parameters Plx 1 Us Z l6 7 16 3 us 7 3 5 FM Pm ll Al 15 quot 7 39 5 Us Che 12 probability for 6 quot6 each oufzomz We 16 Definitions Z Random Variable a variable typically represented by x that has a single numerical value determined by chance for each outcome of a procedure ZProbability Distribution a graph table or formula that gives the probability for each value of the random variable Table 471 Probability Distribution Number of Girls Among Fourteen Newborn Babies mmummbunao R o o m Definitions ozoDiscrete random variable has either a finite number of values or countable number of values where countable refers to the fact that there might be infinitely many values but they result from a counting process ozoContinuous random variable has infinitely many values and those values can be associated with measurements on a continuous scale with no gaps or interruptions Figure473 otzsvsa7svwnrztam Number cl 0w amang Faurmnn wams Requirements for Probability Distribution 2Px1 where x assumes all possible values Requirements for Probability Distribution 2Px1 where x assumes all possible values OsPxs1 for every value of x Mean Variance and Standard Deviation of a Probability Distribution Formula 41 H 239 x F x Formula 42 oz 2 x uf Px Formula 43 0392 Z x2 Px 112 shortcut Mean Variance and Standard Deviation of a Probability Distribution Formula 41 H 2 x Px Formula 42 oz 2 x uf Px Formula 43 0392 2 x2 Px 112 shortcut Formula 44 039 IV szPx 112 Usual Sample Values minimum u 2a maximum u 2a Table 41 Probability Distribution Number of Girls Among Fourteen Newborn Babies 1 g wNAomemmlsz HD o N N Usual Sample Values minimum 70 21876 3248 maximum 70 21876 10752 Using the Rare Event Rule If under a given assumption such as the assumption that boys and girls are equally likely the probability of a particular observed event such as 13 girls in 14 births is extremely small we conclude that the assumption was probably not correct boys and girls NOT equally likely the gender selection technique did have an effect Using Probabilities to Determine When Results Are Unusual Xis unusually high if with x successes among n trials Px or more is very small such as 005 or less X is unusually low if with x successes among n trials Px or fewer is very small such as 005 or less Table 41 Probability Distribution Number of Girls Among Fourteen Newborn Babies 1 g wNAomemmlsz HD o N N Definition Expected Value The average value of outcomes E 2 x Px E Z x 0 Px Event x Px Win 499 0001 Lose 1 0999 Measures of Relative Standing Position Section 26 Measures of Relative Standing Position 3 Z Score or standard score the number of standard deviations that a given value x is above or below the mean Measures of Position 2 score Sample x3 239 s Measures of Position Z score Sample Population 2 x f z x S 039 Measures of Position Z score Sample Population 2 x f z x S 039 Round to 2 decimal places FIGURE 214 Interpreting Z Scores Unusual Ordinary Unusual Values Values Values I I I I I 3 2 1 0 1 2 3 Z Other Measures of Position Quartiles Percentiles Quartiles Q1 02 03 divides ranked scores into four equal parts 25 25 25 25 minimum Q1 Q2 Q3maximum median Percentiles 99 Percentiles P P quotPasng Finding the Percentile of a Given Score number of scores less than X Percentile of score X o 100 total number of scores Finding the Score Given a Percentile 11 total number of values in the data set k k percentile being used O 100 L locator that gives the position of a value Pk kth percentile Sortthedata Arrange the data in orrlowest to I kth Percentile n number of value k percentile in question The value of the kth percentile is midway between the Lth value and the next value in the next value and dividing the tota by2 cnange L by rounding it up to the next largerwnole number Figure 215 The value of Pk is the Lth value counting from the lowest Elementary Probability and Statistics MATH 1530 Cheryl 5 Slaydon Assoclate Professor of Mathematlcs Some Graphlcs by Bob Maschak Media Spaclallst L L LLL L L Permission has been granted by PearsonAddisonWesley Publishing Company for use of the graphics and text problems from Elementam Statistics and Essentials of Statistics by Mario F Triola L y LLL L L Chapter 1 Introduction to Statistics 11 Overview 12 Types of Data 13 Critical Thinking 14 Design of Experiments L y LLL L L 11 Overview Statistics Two Meanings Z Method of analysis Z Specific numbers Statistics t Method of analysis a collection of methods for planning experiments obtaining data and then organizing summarizing presenting analyzing interpreting and drawing conclusions based on the data Statistic 2 Specific number numerical measurement describing some characteristic of a sample Example Twentythree percent of people polled believed that there are too many polls Definitions tData observations such as measurements genders survey responses that have been collected Definitions tPopulation the complete collection of all elements scores people measurements and so 0 studied The collection is complete in the sense that it includes all subjects to be studied Definitions tCensus the collection of data from every element in a population tSample a subcollection of elements drawn from a population 12 Types of Data Definitions 20 Parameter a numerical measurement describing some characteristic of a population population parameter Definitions 20 Statistic a numerical measurement describing some characteristic of a sample sample statistic Definitions tQuantitative Data numbers representing counts or measurements 1 Qualitative or categorical or attribute Data can be separated into different categories that are distinguished by some nonnumerical characteristic m V min 13 Definitions tQuantitative Data the incomes of college graduates 1 Qualitative or categorical or attribute Data the genders malefemale of college graduates m V min A Definitions tDiscrete data result when the number of possible values is either a finite number or a countable39 number of possible Va ues o 1 2 3 t Continuous numerical data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps interruptions orjumps 3 m V min 15 Definitions tDiscrete The number of eggs that hens lay for example 3 eggs a day t Continuous The amounts of milk that cows produce for example 2343115 gallons a day m l my 15 Levels of Measurement 2 Nominal 2 Ordinal 2 Interval 2 Ratio m l min 17 Definitions 2 nominal level of measurement characterized by data that consist of names labels or categories only The data cannot be arranged in an ordering scheme such as low to high Example survey responses yes no undecided m l ml is Definitions 2 ordinal level of measurement involves data that can be arranged in some order but differences between data values either cannot be determined or are meaningless Example Course grades A B C D or F m V min a Definitions 3 interval level of measurement like the ordinal level with the additional property that the difference between any two data values is meaningful However there is no natural zero starting point where none of the quantity is present Example Years 1000 2000 1776 and 1492 m V my 2 Definitions 2 ratio level of measurement the interval level modified to include the natural zero starting point where zero indicates that none of the quantity is present For values at this level differences and ratios are meaningful Example Prices of college textbooks m V min 21 Levels of Measurement 2 Nominal categories only 2 Ordinal categories with some order 2 Interval differences but no natural ta 39 g point 2 Ratio differences M a natural starting point m y Hiva 22 Section 13 Critical Thinking Z Almost all fields of study benefit from the application of statistical methods m y Hiva 2 Critical Thinking 2Bad Samples selfselected survey or voluntary response sample one in which the respondents themselves decide whether to be included m y vavA 2A Critical Thinking 2 Voluntary Response Samples 2 Small Samples 2 Graphs Salaries of People with Bachelor s Degrees and with High School Diplomas 40000 40000 35000 30000 30000 20000 25000 10000 20000 Bachelor HI9h5ch l Eachelor nghschool Dlploma Degree Dlplollla e y Mia b 25 We should analyze the numerical information given in the graph instead of being mislead by its general shape Salaries of People with Bachelor s Degrees and with High School Diplomas 40000 30000 Bachelor High School Bachelor High School Degree Diploma Degree Diploma a Chaplerl Semnn171172173174 noaEssenualsnfStaumcsSecnndEdmnn cnpynm 2004 Pearson ddisnanesley 7 3 Critical Thinking 0 0 Voluntary Response Samples 0 SmallSamples Graphs Pictographs 9 9 9 0 9 0 Chaplerl Semnn171172173174 TnnlaEssenualsnfStaumcsSecnndEdmnn cnpynm 2004 PearsonAddisoanesley 2 3 Double the lenth width and heiht of a cube and the volume increases by a factor of eiht Chaplerl Semnn171172173174 TnnlaEssenualsnfStaumcsSecnndEdmnn cnpynm 2004 PearsonAddisoanesley 30 N0 Critical Thinking 1 Voluntary Response Samples 1 Small Samples 1 Graphs 1 Pictographs 1 Percentages 1 Loaded Questions 1 Order of Questions 1 Refusals 00 Etc m y my 1 Section 14 Design of Experiments m y my 32 Two Major Points oz If sample data are not collected in an appropriate way the data may be completely useless oz Randomness typically plays a crucial role in determining which data to collect m y my 33 111 Definitions 439 Observational Study observing and measuring specific characteristics without attempting to modify the subjects being studied m V min at Definitions 439 Experiment apply some treatment and then observe its effects on the subjects m V min 35 Designing an Experiment 39239 Identify your objective 39239 Collect sample data 39239 Use a random procedure that avoids bias 39239 Analyze the data and form conclusions m V min as 122 Definitions t Confounding occurs in an experiment when the effects from two or more variables cannot be distinguished from each other Definitions t Replication used when an experiment is repeated on a sample of subjects that is large enough so that we can see the true nature of any effects instead of being misled by erratic behavior of samples that are too small Randomization and Other Sampling Strategies t Random Sample when members from the population are selected in such a way that each individual member has an equal chance of being selected 133 Randomization and Other Sampling Strategies t Simple Random Sample when size n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen Random sampling selection so that each has an equal chance of being selected Systematic Sampling Select some starting point and then select every Kth element in the population m m m Example Every third person 114 Convenience Sampling use results that are readily available Hey Do you believe in the death penalty Chapter 1 Section 11121314 Triola Essentials of Statistics Second Edition Copyright 2004 PearsonAddisonWesley 4393 Stratified Sampling subdivide the population into subgroups that share the same characteristic then draw a sample from each e 23 mg 2 Kai Chapter 1 Section 11121314 Triola Essentials of Statistics Second Edition Copyright 2004 PearsonAddisonWesley 44 Cluster Sampling divide the population into sections or clusters randomly select some of those clusters choose aH members from selected clusters Chapter 1 Section 11121314 Triola Essentials of Statistics Second Edition Copyright 2004 PearsonAddisonWesley 155 Waiting Times of Bank Customers at Different Banks in minutes Measures of Variation IJefferson ValleyBank I 65 66 67 68 71 73 74 77 77 77 I I Bank of Providence I 42 54 58 62 67 77 77 85 93 100 Section 25 Waiting Times of Bank Customers D tp ts 0f waiting Times at D 39ffe rent Ban k5 Jefferson Valley Bank singe wamng 1mg In minutes Mean715 Median 720 Mode 77 IJeffersonValleyBankIG5 66 61 68 11 13 14 11 11 11 I Midrange7r10 I Bank of Providence I 42 54 58 62 67 77 77 85 93 100 I I I y I f 5 6 7 K 9 10 Jefferson Valley Bank Bank of Providence o u n 39 o o o 39 o 39 s i 0 Mean 5 715 Bank of 7 rovrdence mumale wai ng lines Median 720 720 Median 720 Mode 77 mode 7397 7397 Midrange710 Midrange 710 710 Measures of Variation Range highest lowest value value Measures of Variation Standard Deviation 20 A measure of variation of the scores about the mean 20 Average deviation from the mean 20 Average distance scores are from the mean Standard Deviation Formula for a Sample Formula 24 Compute the standard deviation for the numbers 12345 by hand and by calculator Important Properties of Standard Deviation 3 A measure of variation of all values from the mean 3 Usually positive is zero 0 when all data are the same v Value can increase dramatically with outliers v Units are the same as the units of the original data Same Means 7 4 Different Standard Deviations m 1234567 1234567 1234567 1234567 Frequency 3 a s 01 rn Same Means 39 4 Different Standard Deviations Frequency 3 a s 01 rn m 1234567 1234567 1234567 1234567 When data is more varied the standard deviation gets Using Your Calculator to find the standard deviation of a data set 65 66 67 68 71 73 74 77 77 77 Using Your Calculator to find the standard deviation of a data set 66 67 68 71 74 77 77 77 S 048 minutes 65 73 Population Standard Deviation o ZoraHY calculators can compute the population standard deviation of data Measures of Variation Variance Measures of Variation Variance standard deviation sguared Measures of Variation Variance standard deviation sguared S 2 use square key Notat n a 2 on calculator Variance 52 M Sample n 1 Variance 2 2 x 39 102 Population 0 N Variance Using Your Calculator to find the standard deviation of a data set 65 66 67 68 71 73 74 77 77 77 S 048 minutes Using Your Calculator to find the standard deviation of a data set 65 66 67 68 71 73 74 77 77 77 S 048 minutes S2 023 minutes2 Notation Sam ple Textbook 5 Some graphics SX calculators Some xan1 nongraphics calculators Notation Sample Population Notation Sample Population Textbook 5 Some graphics gt SX calculators Som e x On1 nong raphics calculators o lt Book Some graphics a x calculators Some XOn nongraphics calculators Textbook 5 Some graphics SX calculators Som e x On1 nong raphics calculators o lt Book Some graphics a x calculators xan Some nong raphics calculators Articles in professional journals and reports often use SD for standard deviation and VAR for variance Estimation of Standard Deviation Range Rule of Thumb EZs J x x25 maxi mum minimum usual value I Range w 45 usual value Estimation of Standard Deviation Range Rule of Thumb 4 E 2 x 2 39 39 maximum III153 s I usual value Range g 45 Range 5 Estimation of Standard Deviation Range Rule of Thumb E 2 x Y 2 minimum I maximum usual value usual value Range a 4s Range highest value lowest value 554 4 Estimating the standard deviation using the Range Rule of Thumb 65 66 67 68 71 73 74 77 77 77 SzRangel477 65l4 124 03 min estimate S 048 minutes actual The Empirical Rule FIGURE 2 13 applies to bellshaped distributions The Empirical Rule FIGURE 2 13 applies to bellshaped distributions 1 standard deviation Chapter 2 Describing Exploring and Comparing Data Chapter 2 Describing Exploring and Comparing Data 21 Overview 22 Frequency Distributions 23 Visualizing Data 24 Measures of Center 25 Measures of Variation 26 Measures of Relative Standing 27 Exploratory Data Analysis EDA 21 Overview Important Characteristics of Data 1 Center A representative or average value that indicates where the middle of the data set is located 2 Variation A measure of the amount that the values vary among themselves 3 Distribution The nature or shape of the distribution of data such as bellshaped uniform or skewed 4 Outliers Sample values that lie very far away from the vast majority of other sample values 5 Time Changing characteristics of the data over time 2 1 Overview 00 Descriptive Statistics summarize or describe the important characteristics of a known set of population data 00 Inferential Statistics use sample data to make inferences or generalizations about a population 22 Frequency Distributions 00 Frequency Table lists data values either individually or by groups of intervals along with their corresponding frequencies or counts Qwerty Keyboard Word Ratings 2 2 5 1 2 6 3 3 4 2 4 0 5 7 7 5 6 6 8 10 7 2 2 10 5 8 2 5 4 2 6 2 6 1 7 2 7 2 3 8 1 5 2 5 2 14 2 2 6 3 1 7 Frequency Table of Qwerty Word Ratings Rating Frequency 02 20 35 14 6 8 15 911 2 12 14 1 Frequency Table De nMons Lower Class Limits are the smallest numbers that can actually belong to different classes Lower Class Limits are the smallest numbers that can actually belong to different classes Rating Frequency 02 20 35 14 6 8 15 911 2 12 14 1 Lower Class Limits are the smallest numbers that can actually belong to different classes Rating Frequency Lower Class 35 14 5 8 15 Upper Class Limits Upper Class Limits are the largest numbers that can actually belong to are the largest numbers that can actually belong to different classes different classes Rating Frequency Rating Frequency 0 2 20 Upper Class r 2 20 35 14 Limits 14 68 15 We 15 911 2 911 2 1214 1 1214 1 Class Boundaries Class Boundaries number separating classes number separating classes Ratinq Frequencv Ratinq Frequencv o 2 20 2 5 o 2 20 35 14 cass 55 35 14 68 15 Boundaries 85 68 15 911 2 911 2 115 1214 1 1214 1 145 Class Midpoints midpoints of the classes Class Midpoints mid points of the classes Rating Frequency Class Midpoints Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Rating Frequency 3 02 20 3 35 14 Class WIdth 3 68 15 3 911 2 3 1214 1 Constructing A Frequency Table Decide on the number of classes Determine the class width by dividing the range by the number of classes and round up usually Highest value lowest value number of classes Select for the rst lower limit either the lowest score or a convenient value slightly less than the lowest score class width 11 Add the class width to the starting point to get the second lower class limit add the width to the second lower limit to get the third and so on List the lower class limits in a vertical column and enter the upper class limits Represent each score by a tally mark in the appropriate class Total tally marks to nd the total frequency for each class Guidelines For Frequency Tables Be sure that the classes are mutually exclusive that is do not overlap so each data value belongs to only one class Include all classes even if the frequency is zero Try to use the same width for all classes although sometimes openended intervals are necessa The sum of the class frequencies must equal the number of original data values Relative Frequency Table class frequency relative sum of all frequencies Relative Frequency Table Rating Frequency 02 35 68 911 1214 20 14 15 2 1 Relative Rating Frequency 02 35 68 911 1214 385 269 288 38 19 Total frequency 52 Total percentage 100 2052 385 1452 269 etc 53 Applications of Normal Distributions Table A2 Standard Normal Distribution Cumulative from left a u 0 a Other Normal Distributions lf at 0 or a39 at 1 or both we will convert values to standard scores using Formula 52 then procedures for working with all normal distributions are the same as those for the standard normal distribution Round to 2 Formula 572 decimal places Converting to Standard Normal Distribution p a Nonstandard b Standard Normal Dlsfr lbutlen Normal Dlsrrlbullon Figure 5 12 Example The sitting height from seat to top of head of drivers must be considered in the design of a new car model Men have sitting heights that are normally distributed with a mean of 360 in and a standard deviation of 14 in based on anthropometric survey data from Gordon Clauser et al Engineers have provided plans that can accommodate men with sitting heights up to 388 in but taller men cannot fit If a man is randomly selected find the probability that he has a sitting height less than 388 in Based on that result is the current engineering design feasible Probability of Sitting Heights Less Than 388 Inches g 360 17 14 X Sitting Height Probability of Sitting Heights Less Than 388 Inches 3eo z 388 360 200 17 14 14 Probability of Sitting Heights Less Than 388 Inches 3eo z 388 360 200 17 14 14 x Sitting Height 350 388 O 200 I Area 09772 X Sitting Height ago 3255 3 2330 I Central Limit Theorem Central Limit Theorem Given Conclusions 1 The distribution of samplefwill as the sample size increases approach a normal distribution 1 The random variable X has a distribution which may or may not be normal with mean I and standard deviation 039 2 Samples all of the same size n are randomly 239 The me Of the sample means WI be the populatlon mean u selected from the populatlon ovaalues 3 The standard deviation of the sample means will approach cVn Practical Rules Notation Commonly Used the mean of the sample means 1 For samples of size n larger than 30 the distribution of the sample means can be approximated reasonably well by a normal distribution The approximation gets better I u as the sample size n becomes larger 2 If the original population is itself normally distributed then the sample means will be normally distributed for any sample size n not just the values of n larger than 30 Notation the mean of the sample means 2 H the standard deviation of sample mean a Notation the mean of the sample means IJ the standard deviation of sample mean we often called standard error of the mean Distribution of 200 digits from Social Security Numbers Last 4 digits from so students N a Frequency 5 O l 2 3 H 3 6 7 K 9 Distribuhan of 200 Dig1 s Figure 519 Distribution of 50 Sample Means for 50 Students 6 G m Frequency 4 s a 7 5 9 Distributlon 01 50 Sumpe Means Figure 520 As the sample size increases the sampling distribution of sample means approaches a normal distribution Example Given the population of men has normally distributed weights with a mean of 172 lb and a standard deviation of 29 lb a if one man is randomly selected nd the probability that his weight is greater than 167 lb b if 12 different men are randomly selected nd the probab II ty that their mean weight is greater than 167 lb Example Given the population of men has normally dist 39buted weights with a mean of 172 lb and a standard devration o 9 b a if one man is randomly selected nd the probability that his weight is greater than 167 lb Z 167 172 017 29 04325 x 1577 72 U 29 Example Given the population of men has normally distributed weights with a mean of 172 lb and a standard de i a I one man is randomly selected the probability that his weight is greater than 167 lb is 05675 X 1677 172 U Z9 Example Given the population of men has normally distributed weights with a mean of 172 lb and a standard deviation of 2 b if 12 ifferent men are randomly selected nd the probability that their mean weight is greater than 167 lb Example Given the population of men has normally distributed weights with a mean of 172 lb and a standard 39 9 b if 12 different men are randomly selected nd the probability that their mean weight is greater than 167 lb 17 z Z7 7 quot smegma Example Given the population of men has normally distributed weights with a mean of 172 lb eviation o b b 39f 12 different men are randomly selected nd 32g 72 060 3 3 Addition Rule Definition 00 Compound Event Any event combining two or more simple events Definition 00 Compound Event Any event combining two or more simple events 00 Notation PA or B P event A occurs g event B occurs g they both occur Compound Event General Rule When finding the probability that event A occurs g event B occurs nd the total number of ways A can occur and the number of ways B can occur but find the total in such a way that no outcome is counted more than once Compound Event Formal Addition Rule PA or B PA PB PA and B where PA and Bi denotes the probability that A and B both occur at the same time Com pound Event Formal Addition Rule PA or B PA PB PA and B where PA and B denotes the probability that A and B both occur at the same time Intuitive Addition Rule To nd PA or B find the sum of the number ofways event A can occur and the number ofways event B can occur addinq in such a wav that everv outcome is counted only once PA or B is equal to that sum divided by the total number of outcomes Definition Events A and B are disjoint or mutually exclusive if they cannot both occur together Definition Events A and B are disjoint or mutually exclusive if they cannot both occur together Total Area 1 PA PB PA and B Overlapping Events Definition Events A and B are disjoint or mutually exclusive if they cannot both occur together Total Area 1 Total Area 1 PA PB PA PB Disjoint events cannot happen at the same time They are separate pA and B nonoverlapping events Overlapping Events Nonoverlapping Events Applying the Addition Rule PA or B PA PB PA and B PA or B Addition Rule Are A and B disjoint 7 PA or B PA PB No O O A Green ball disjoint O B Blue ball eVentS O O disjoint events 0 A Green ball 0 B Blue ball 00 PAorBPAPB 18 Q A Even number A Even number notdisjoint 9 B Number greater 9 B Number greater zngttsehstzv ee CD rm 5 CD ms counted twice counted twice 6 2 Q A Even number Overlapping A Even number Overlapping events some events some B Number greater counted twice 9 B Number greater counted twice than 5 than 5 P005 or B mg PB Em andl B 10 10 39 1o amp counted twice counted twice Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 W 45 2223 Find the probability of randomly selecting a man or a boy Find the probability of randomly selecting a man or a boy Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 W 45 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 W 45 Find the probability of randomly selecting a man or a boy Pman or boy 1692 64 1756 0790 2223 2223 2223 Find the probability of randomly selecting a man or a boy Pman or boy 1692 64 1756 o79o 2223 2223 2223 Disjoint Events Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 Contingency Table n i 39ls Totals 318 29 27 10 35 18 Total 1692 422 64 45 2223 Find the probability of randomly selecting a man or omeone who survived Find the probability of randomly selecting a man or omeone who surv ved Contingency Table Contingency Table 39ls Totals m 318 29 27 35 IA 35 18 rv Total 1692 422 64 45 Find the probability of randomly selecting a man or someone who survived Pman or survivor 1692 706 32 2066 o 929 2223 2223 2223 2223 Find the probability of randomly selecting a man or someone who survived Pman or survivor 1692 706 332 2066 o 929 2223 2223 2223 2223 NOT Disjoint Events Contingency Table Total 1692 422 64 45 2223 Find the probability of randomly selecting a man or someone who survived Pman orsurvivor 1692 706 32 2066 o929 2223 2223 2223 2223 Overlapping Events Setting up a Contingency Table Example In a test of the allergy drug Seldane 49 of 781 users experienced headaches 49 of 665 placebo users experienced headaches and 24 of 626 people in the control group experienced headaches Setting up a Contingency Table Example In a test of the allergy drug Seldane 49 of 781 users experienced headaches 49 of 665 placebo users experienced headaches and 24 of 626 people in the control group experienced headaches Seldane Placebo Control Group Headache 49 49 24 122 No Headache 732 616 602 1950 Totals 781 Setting up a Contingency Table Example In a test of the allergy drug Seldane 49 of 781 users experienced headaches 49 of 665 placebo users experienced headaches and 24 of 626 people in the control group experienced headaches Seldane Placebo Control Group Headache 49 49 24 122 No Headache 732 616 602 1950 Totals 781 665 626 I 2072 Complementary Events PA and PA are disjoint Complementary Events PA and PA are disjoint All simple events are either in A or K Complementary Events PA and PA are disjoint All simple events are either in A or K PA PK 1 Rules of Complementary Events PA PA 1 PA 1 PA PA 1 PA

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.