Lecture Business statistics in practice (7/e): Chapter 6 - Bowerman, O’Connell, Murphree

Chapter 6 - Continuous random variables. After mastering the material in this chapter, you will be able to: Define a continuous probability distribution and explain how it is used, use the uniform distribution to compute probabilities, describe the properties of the normal distribution and use a cumulative normal table, use the normal distribution to compute probabilities,...
Nội dung trích xuất từ tài liệu:
Lecture Business statistics in practice (7/e): Chapter 6 - Bowerman, OConnell, Murphree Chapter6 ContinuousRandomVariablesMcGrawHill/Irwin Copyright©2014byTheMcGrawHillCompanies,Inc.Allrightsreserved.ContinuousRandomVariables6.1ContinuousProbabilityDistributions6.2TheUniformDistribution6.3TheNormalProbabilityDistribution6.4 ApproximatingtheBinomialDistribution byUsingtheNormalDistribution (Optional)6.5 TheExponentialDistribution(Optional)6.6 TheNormalProbabilityPlot(Optional) 62LO6-1: Define acontinuous probabilitydistribution and explainhow it is used. 6.1ContinuousProbability Distributions Acontinuousrandomvariablemayassume anynumericalvalueinoneormoreintervals ◦Forexample,timespentwaitinginline Useacontinuousprobabilitydistributionto assignprobabilitiestointervalsofvalues Thecurvef(x)isthecontinuousprobability distributionoftherandomvariablexifthe probabilitythatxwillbeinaspecified intervalofnumbersistheareaunderthe curvef(x)correspondingtotheinterval 63LO6-1 PropertiesofContinuousProbability Distributions  Propertiesoff(x):f(x)isacontinuous functionsuchthat 1. f(x)≥0forallx 2. Thetotalareaunderthef(x)curveisequalto1  Essentialpoint:Anareaunderacontinuous probabilitydistributionisaprobability 64LO6-2: Use the uniformdistribution to computeprobabilities. 6.2TheUniformDistribution  Ifcanddarenumbersontherealline(cLO6-3: Describe theproperties of the normaldistribution and use acumulative normaltable. 6.3TheNormalProbability Distribution Thenormalprobabilitydistributionis definedbytheequation 2 1 x 1 2 f( x) = e σ 2π forallvaluesxontherealnumberline ◦σisthemeanandσisthestandarddeviation ◦π=3.14159…ande=2.71828isthebaseof naturallogarithms 66LO6-3 TheStandardNormalTable Thestandardnormaltableisatablethatlists theareaunderthestandardnormalcurveto therightofnegativeinfinityuptothezvalue ofinterest ◦Table6.1 ◦Otherstandardnormaltableswilldisplaythearea betweenthemeanofzeroandthezvalueof interest Alwayslookattheaccompanyingfigurefor guidanceonhowtousethetable 67LO6-4: Use the normaldistribution to computeprobabilities. FindP(0≤z≤1)  Findthearealistedinthetablecorrespondingtoaz valueof1.00  Startingfromthetopofthefarleftcolumn,go downto“1.0”  Readacrosstherowz=1.0untilunderthecolumn headedby“.00”  Theareaisinthecellthatistheintersectionofthis rowwiththiscolumn  Aslistedinthetable,theareais0.8413,so  P(– ≤z≤1)=0.8413  P(0≤z≤1)=P(– ≤z≤1)–0.5000=0.3413 68LO6-5: Find populationvalues that correspondto specified normal FindingNormalProbabilitiesdistribution probabilities. 1. Formulatetheproblemintermsofxvalues 2. Calculatethecorrespondingzvalues,andrestate theproblemintermsofthesezvalues 3. Findtherequiredareasunderthestandardnormal ...