数据分析2(1)

Whichofthefollowingstatesthattheproportionofoccurrenceswithaparticularoutcomeconvergestotheprobabilityofthatoutcome?YourAnswerScoreExplanationLawoflargenumbersCorrect1.00LawofaveragesGeneraladditionruleBayes’theoremTotal1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:Explainwhythelong-runrelativefrequencyofrepeatedindependenteventssettlesdowntothetrueprobabilityasthenumberoftrialsincreases,i.e.whythelawoflargenumbersholds.Question2ShownbelowarefourVenndiagrams.InwhichofthediagramsdoestheshadedarearepresentAandBbutnotC?YourAnswerScoreExplanationCorrect1.00WeneedtheareacommontoeventsAandBtobeentirelyshadedexceptforthatportioncommontoeventC:“AandBbutnotC”.Total1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:DrawVenndiagramsrepresentingeventsandtheirprobabilities.Question3Eachchoicebelowshowsasuggestedprobabilitydistributionforthemethodofaccesstoonlinecoursematerials(desktopcomputer,laptopcomputer,tablet,smartphone).Determinewhichisaproperprobabilitydistribution.YourAnswerScoreExplanationdesktopcomputer:0.15,laptopcomputer:0.50,tablet:0.30,smartphone:0.20desktopcomputer:0.25,laptopcomputer:0.35,tablet:0.15,smartphone:0.25Correct1.00Sumofallprobabilitiesmustequal1andeachprobabilitymustbeavaluebetween0and1.desktopcomputer:0.20,laptopcomputer:0.20,tablet:0.20,smartphone:0.20desktopcomputer:0.30,laptopcomputer:0.40,tablet:0.35,smartphone:-0.05Total1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:Defineaprobabilitydistributionasalistofthepossibleoutcomeswithcorrespondingprobabilitiesthatsatisfiesthreerules:-Theoutcomeslistedmustbedisjoint.-Eachprobabilitymustbebetween0and1.-Theprobabilitiesmusttotal1.Question4Lastsemester,outof170studentstakingaparticularstatisticsclass,71studentswere“majoring”insocialsciencesand53studentsweremajoringinpre-medicalstudies.Therewere6studentswhoweremajoringinbothpre-medicalstudiesandsocialsciences.Whatistheprobabilitythatarandomlychosenstudentismajoringinpre-medicalstudies,giventhats/heismajoringinsocialsciences?YourAnswerScoreExplanation6/536/1706/71Correct1.00IfMistheeventastudentismajoringinpre-medicalstudiesandSistheevents/heismajoringinsocialsciences,thencalculateP(M|S)=P(M&S)P(S)=671.(71+53−6)/170Total1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:Distinguishmarginalandconditionalprobabilities.Question5Whichofthefollowingisfalse?YourAnswerScoreExplanationIftwooutcomesofarandomprocess(bothwithprobabilitygreaterthan0)aremutuallyexclusive,theyarenotnecessarilycomplements.Iftwoevents(bothwithprobabilitygreaterthan0)aremutuallyexclusive,theycouldbeindependent.Correct1.00Mutuallyexclusiveeventsmaybecomplements(e.g.ifacoinisflippedtheprobabilityofaHeadandaTailareboth0.5,addingupto1)buttheyalsomightnotbeiftherearemorethantwopossibleoutcomesoftherandomprocess(e.g.avotermightbeDemocrat,Republican,orIndependent,sincebeingDemocratandRepublicanaremutuallyexclusivebutnotcomplements).Howevermutuallyexclusiveeventscannotbeindependent;theeventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.Iftheprobabilitiesoftwomutuallyexclusiveoutcomesofarandomprocessaddupto1,theyarecomplements.WhencomputingtheprobabilitythatacarddrawnrandomlyfromastandarddeckiseitheraJackora4,youcanusetheadditionrule.Total1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:•Definedisjoint(mutuallyexclusive)eventsaseventsthatcannotbothhappenatthesametime:IfAandBaredisjoint,P(AandB)=0.•Distinguishbetweendisjointandindependentevents.-IfAandBareindependent,thenhavinginformationonAdoesnottellusanythingaboutB(andviceversa).-IfAandBaredisjoint,thenknowingthatAoccurstellsusthatBcannotoccur(andviceversa).-Disjoint(mutuallyexclusive)eventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.Question6Heightsof10year-olds,regardlessofgender,closelyfollowanormaldistributionwithmean55inchesandstandarddeviation6inches.Whichofthefollowingistrue?YourAnswerScoreExplanationAnormalprobabilityplotofheightsofarandomsampleof50010year-oldspeopleshouldshowafairlystraightline.Correct1.00Sincethedistributionofheightsof10year-oldscloselyfollowanormaldistributionwewouldexpectthenormalprobabilityplotofheightsofalargesampleofsuchkidstoshowastraightline.Roughly95%of10year-oldsarebetween37and73inchestall.Wewouldexpectmore10year-oldstobeshorterthan55inchesthantaller.A10year-oldwhois65inchestallwouldbeconsideredmoreunusualthana10year-oldwhois45inchestall.Total1.00/1.00QuestionExplanationThisquestionreferstothefollowinglearningobjective:UsetheZscore-ifthedistributionisnormal:todeterminethepercentilescoreofadatapoint(usingtechnologyornormalprobabilitytables)-regardlessoftheshapeofthedistribution:toassesswhetherornottheparticularobservationisconsideredtobeunusual(morethan2standarddeviationsawayfromthemean).Question7TheNationalVaccineInformationCenterestimatesthat90%ofAmericanshavehadthediseasechickenpoxbythetimetheyreachadulthood.Whatistheprobabilitythatexactly92outof100randomlysampledAmericanad