数据分析21Word文档格式.docx

数据分析21Word文档格式.docx

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QuestionExplanationThisquestionreferstothefollowinglearningobjective:

Explainwhythelong-runrelativefrequencyofrepeatedindependenteventssettlesdowntothetrueprobabilityasthenumberoftrialsincreases,i.e.whythelawoflargenumbersholds.

Question2

ShownbelowarefourVenndiagrams.InwhichofthediagramsdoestheshadedarearepresentAandBbutnotC?

WeneedtheareacommontoeventsAandBtobeentirelyshadedexceptforthatportioncommontoeventC:

“AandBbutnotC”.

DrawVenndiagramsrepresentingeventsandtheirprobabilities.

Question3

Eachchoicebelowshowsasuggestedprobabilitydistributionforthemethodofaccesstoonlinecoursematerials（desktopcomputer,laptopcomputer,tablet,smartphone）.Determinewhichisaproperprobabilitydistribution.

desktopcomputer:

0.15,laptopcomputer:

0.50,tablet:

0.30,smartphone:

0.20

0.25,laptopcomputer:

0.35,tablet:

0.15,smartphone:

0.25

Sumofallprobabilitiesmustequal1andeachprobabilitymustbeavaluebetween0and1.

0.20,laptopcomputer:

0.20,tablet:

0.20,smartphone:

0.30,laptopcomputer:

0.40,tablet:

0.35,smartphone:

-0.05

Defineaprobabilitydistributionasalistofthepossibleoutcomeswithcorrespondingprobabilitiesthatsatisfiesthreerules:

-Theoutcomeslistedmustbedisjoint.

-Eachprobabilitymustbebetween0and1.

-Theprobabilitiesmusttotal1.

Question4

Lastsemester,outof170studentstakingaparticularstatisticsclass,71studentswere“majoring”insocialsciencesand53studentsweremajoringinpre-medicalstudies.Therewere6studentswhoweremajoringinbothpre-medicalstudiesandsocialsciences.Whatistheprobabilitythatarandomlychosenstudentismajoringinpre-medicalstudies,giventhats/heismajoringinsocialsciences?

6/53

6/170

6/71

IfMistheeventastudentismajoringinpre-medicalstudiesandSistheevents/heismajoringinsocialsciences,thencalculateP（M|S）=P（M&

S）P（S）=671.

（71+53−6）/170

Distinguishmarginalandconditionalprobabilities.

Question5

Whichofthefollowingisfalse?

Iftwooutcomesofarandomprocess（bothwithprobabilitygreaterthan0）aremutuallyexclusive,theyarenotnecessarilycomplements.

Iftwoevents（bothwithprobabilitygreaterthan0）aremutuallyexclusive,theycouldbeindependent.

Mutuallyexclusiveeventsmaybecomplements（e.g.ifacoinisflippedtheprobabilityofaHeadandaTailareboth0.5,addingupto1）buttheyalsomightnotbeiftherearemorethantwopossibleoutcomesoftherandomprocess（e.g.avotermightbeDemocrat,Republican,orIndependent,sincebeingDemocratandRepublicanaremutuallyexclusivebutnotcomplements）.Howevermutuallyexclusiveeventscannotbeindependent;

theeventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.

Iftheprobabilitiesoftwomutuallyexclusiveoutcomesofarandomprocessaddupto1,theyarecomplements.

WhencomputingtheprobabilitythatacarddrawnrandomlyfromastandarddeckiseitheraJackora4,youcanusetheadditionrule.

•Definedisjoint（mutuallyexclusive）eventsaseventsthatcannotbothhappenatthesametime:

IfAandBaredisjoint,P（AandB）=0.

•Distinguishbetweendisjointandindependentevents.

-IfAandBareindependent,thenhavinginformationonAdoesnottellus

anythingaboutB（andviceversa）.

-IfAandBaredisjoint,thenknowingthatAoccurstellsusthatBcannotoccur（andviceversa）.

-Disjoint（mutuallyexclusive）eventsarealwaysdependentsinceifoneeventoccursweknowtheotheronecannot.

Question6

Heightsof10year-olds,regardlessofgender,closelyfollowanormaldistributionwithmean55inchesandstandarddeviation6inches.Whichofthefollowingistrue?

Anormalprobabilityplotofheightsofarandomsampleof50010year-oldspeopleshouldshowafairlystraightline.

Sincethedistributionofheightsof10year-oldscloselyfollowanormaldistributionwewouldexpectthenormalprobabilityplotofheightsofalargesampleofsuchkidstoshowastraightline.

Roughly95%of10year-oldsarebetween37and73inchestall.

Wewouldexpectmore10year-oldstobeshorterthan55inchesthantaller.

A10year-oldwhois65inchestallwouldbeconsideredmoreunusualthana10year-oldwhois45inchestall.

UsetheZscore

 -ifthedistributionisnormal:

todeterminethepercentilescoreofadatapoint（usingtechnologyornormalprobabilitytables）

 -regardlessoftheshapeofthedistribution:

toassesswhetherornottheparticularobservationisconsideredtobeunusual（morethan2standarddeviationsawayfromthemean）.

Question7

TheNationalVaccineInformationCenterestimatesthat90%ofAmericanshavehadthediseasechickenpoxbythetimetheyreachadulthood.Whatistheprobabilitythatexactly92outof100randomlysampledAmericanadultshadchickenpoxduringchildhood?

0.07

0.02

0.14

0.11

Usethebinomialdistributionwithn=100,k=92,andp=0.9.ThenP（k=92）=（）0.9920.18=0.114892

0.10

Calculatetheprobabilityofagivennumberofsuccessesinagivennumberoftrialsusingthebinomialdistribution.

Question8

YourroommatelovestoeatChinesefoodfordinner.Heestimatesthatonanygivennight,there’sa30%chancehe’llchoosetoeatChinesefood.AlthoughhelovesChinesefood,hedoesn’tliketoeatittoomuchinashortperiodoftime,soonmostweeksheeatsseveraldifferentkindsoffoodsfordinner.Supposeyouwantedtocalculatetheprobabilitythat,overthenext7days,youfriendeatsChinesefoodatleast3times.Whichofthefollowingisthemostaccuratestatementaboutcalculatingthisprobability?

Becausewedonotknowtheprobabilitiesofyourroommateeatinganyothertypesoffoods,wecannotusethebinomialdistributiontocalculatethedesiredprobability.

Because“success”or“failure”havenorealmeaninginthecontextofthisproblem,wecannotusethebinomialdistributiontocalculatethedesiredprobability.

Becausehedoesn’tliketoeatChinesefoodtoomuchinashortperiodoftime,pisnotreallythesameforeachtrialandsowecannotusethebinomialdistributiontocalculatethedesiredprobability.

Becauseweknown=3,k=7,andp=0.30,wecanusethebinomialdistributiontocalculatethedesiredprobability.

Becauseweknown=7,k=3,andp=0.30,wecanusethebinomialdistributiontocalculatethedesiredprobability.

Inorrect

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Determineifarandomvariableisbinomialusingthefourconditions.

 -Thetrialsareindependent.

 -Thenumberoftrials,n,isfixed.

 -Eachtrialoutcomecanbeclassifiedasasuccessorfailure.

 -Theprobabilityofasuccess,p,isthesameforeachtrial.

Question9

Whichofthefollowing,onitsown,istheleastusefulmethodforassessingifthedatafollowanormaldistribution?

Checkifthepointsareonastraightlineonanormalprobabilityplot.

Checkif68%ofthedataarewithin1SDofthemean,95%ofdataarewithin2SDsofthemean,and99.7%ofdataarewithin3SDsofthemean.

Checkifthedistributionisunimodalandsymmetric.

Allofthesearefeasiblemethodsforcheckingfornormalityofadistribution,buttheleastusefuliswhetherthemeanandmedianareequalsincethiswillbetrueforanysymmetricdistributionregardlessofwhetherit’snormalornot.Forexample,imagineaperfectlysymmetricbimodaldistribution（likeanmshape）,themeanandthemedianofthisdistributionwillbeequalhowevertheshapeiscertainlynotnormal.

Checkifthemeanandmedianareequal.

Assesswhetherornotadistributionisnearlynormalusingthe68-95-99.7%ruleorgraphicalmethodssuchasanormalprobabilityplot.

Question10

Whichofthefollowingistrue?

Hint:

Itmightbeusefultosk