Slide 1ExamTopicsTopicsExamplesExample 1 (cont)Example 1 (Cont)PopulationExample 1Z Score Steps©Z ExampleZ ExampleZ ExampleSlide 14Relative Frequency and ProbabilityJoint ProbabilityProbabilityContingency TableContingency TableQuestions?Exam 1 ReviewExam •27 Questions•Problems•Fill in the blank•Short Answer•200 points•Everything discussed so far•Read the question!!!Topics•Decision Making•Decision Making Models•Ethics•Sampling•Graphs and Data Display•Mean, Median, Mode•Normal Distribution•Frequency•Relative Frequency•Class Width/Class Boundaries•Probability•Discrete Random Variables•Continuous Random VariablesTopics •Cumulative Relative Frequency•Mean, Median, Mode•Z tables•Z Scores – Probability from Z ScoresExamples485 136 246489 135 194567 132 265567 124 269551 158 237Mean = (∑ all data/15)= 4555/15 = 303.66Example 1 (cont)124132135136158194237246265269485489551567567485 136 246489 135 194567 132 265567 124 269551 158 237Median = 246Mode = ?Symmetrical ?Example 1 (Cont)XaveX-AVE (x-ave)2124 303.66 -179.66 32278132 303.66 -171.66 29467135 303.66 -168.66 28446136 303.66 -167.66 28110158 303.66 -145.66 21217194 303.66 -109.66 12025237 303.66 -66.66 4443.6246 303.66-57.66 3324.7265 303.66 -38.66 1494.6269 303.66 -34.66 1201.3485 303.66 181.34 32884489 303.66 185.34 34351551 303.66 247.34 61177567 303.66 263.34 69348567 303.66 263.34 69348 Variance30651 Std Dev175.07Population XaveX-AVE (x-ave)2124 303.66 -179.66 32278132 303.66 -171.66 29467135 303.66 -168.66 28446136 303.66 -167.66 28110158 303.66 -145.66 21217194 303.66 -109.66 12025237 303.66 -66.66 4443.6246303.66-57.66 3324.7265 303.66 -38.66 1494.6269 303.66 -34.66 1201.3485 303.66 181.34 32884489 303.66 185.34 34351551 303.66 247.34 61177567 303.66 263.34 69348567 303.66 263.34 69348 Variance28608 Std Dev169.14Example 1•Coefficient of variation:•Standard deviation over mean•169.14/303.66•.557 x 100 = 55.7%Z Score Steps©•Draw the curve•Determine point of interest (x or x)•Calculate z: x-µ σ•Look up the probability associated with Z score•Do I need to add or subtract?•Determine probabilityZ Example•Mean = 303.66•Std dev = 169.14•Z = (x-µ)/std dev•P(x ≥ 375)•Z = (375-303.66)/169.14•Z = 0.42•Z table•Where are we in the curve?•Probability =Z Example•Mean = 303.66•Std dev = 169.14•Z = (x-µ)/std dev•P(x ≤ 475)•Z = (475-303.66)/169.14•Z = 1.01•Z table•Where are we in the curve?•Probability =Z Example•Mean = 303.66•Std dev = 169.14•Z = (x-µ)/std dev•P(250 ≤ x ≤ 475)•Z1 = (250-303.66)/169.14•Z1 = -0.32•Z2 = (475-303.66)/169.14•Z2 = 1.01•Z table•Where are we in the curve?•Probability =Number of days read FrequencyRelative Frequency0 4444/2001 2424/2002 1818/2003 1616/2004 2020/2005 2222/2006 2626/2007 3030/200Total 200Number of days readFrequencyRelative Frequency Probability0 4444/200 0.221 2424/200 0.122 1818/200 0.093 1616/200 0.084 2020/200 0.15 2222/200 0.116 2626/200 0.137 3030/200 0.15Total 200 1Relative Frequency and ProbabilityJoint Probability•Probability of two independent events taking place•= P(E1) x P(E2)•Craps table •P(4 on die 1) and P(4 on die 2)•= 1/6 x 1/6•= 1/36Probability •P(rolling 4) = P(11 and 32)+ P(21 and 22) + P (31 and 12)= 3/36•P(rolling 8) = P(6 and 2) + P(5 and 3) + P(4 and 4) + P(3 and 5) + P(2 and 6) = _________Contingency TableProduct/color Blue Yellow RedFiesta 150 45 300Focus 200 15 4501.Add all the rows2.Add all the columnsContingency Table Product/Color Blue Yellow Red TotalsFiesta 150 45 300 495Focus 200 15 450 665Totals 350 60 750 11601. What is the probability that the car will be a Fiesta? 495/11602. What is the probability that it will be a yellow Focus? 15/11603. What is the probability that the car will be both yellow and red?