IntrotoStatisticsFall2017–MidtermName:

1. True/FalseQuestions–Iffalse,stateyourreasonwhyormakeitatruestatement.

a. Aprobabilityof0.1indicatesanunusualevent.�

b. Whenaneventisalmostcertaintohappen,itscomplementwillbeanunusual

event.

c. Whentwoeventsaremutuallyexclusive,theyhavenooutcomesincommon.

d. Whentwoeventsareindependent,theyarealsomutuallyexclusive.�

e. Acombinationisanorderedarrangementofobjects.�

f. Thenumberofdifferentorderedarrangementsofndistinctobjectsisn!

g. Themeanoftherandomvariableofaprobabilitydistributiondescribeshowthe

outcomesvary.�

h. Theexpectedvalueofarandomvariablecanneverbenegative.

i. Thevarianceofarandomvariablecanneverbenegative.

j. Anexperimentisaprocesswhoseoutcomecanbepredictedwithcertainty.

2. Usethetable,whichshowstheapproximatedistributionofthesizesoffirmsforarecentyear.

a. Findtheprobabilitythatarandomlyselectedfirmwillhaveatleast10employees.

b. Findtheprobabilitythatarandomlyselectedfirmwillhavefewerthan20employees.

3. Acardisrandomlyselectedfromastandarddeckof52playingcards.Findtheprobabilitythatthecardisredoraqueen.

4. Abatchof200calculatorscontains3defectiveunits.Whatistheprobabilitythatasampleofthreecalculatorswillhave(a)nodefectivecalculators?(b)alldefectivecalculators?(c)atleastonedefectivecalculator?(d)atleastonenon-defectivecalculator?

5. Findthea. meanb. variancec. standarddeviationoftheprobabilitydistributiond. interprettheresults.

Thenumberofcellphonesperhouseholdinasmalltown.

6. Findtheindicatedbinomialprobabilities.Thirty-fourpercentofU.S.adultspersonallyownagun.Yourandomlyselect12U.S.adults.FindtheprobabilitythatthenumberofU.S.adultswhosaytheypersonallyownagunis(a)exactlytwo(b)atleasttwo(c)morethantwo.

7. Twenty-twopercentofformersmokerssaytheytriedtoquitfourormoretimesbeforetheywerehabit-free.Yourandomlyselect10formersmokers.Findtheprobabilitythatthefirstpersonwhotriedtoquitfourormoretimesis(a)thethirdpersonselected(b)thefourthorfifthpersonselected(c)notoneofthefirstsevenpeopleselected.

8. Findtheareaoftheindicatedregionunderthestandardnormalcurve.

9. Findtheareaoftheindicatedregionunderthestandardnormalcurve.

10. Findtheindicatedareaunderthestandardnormalcurve.Ifconvenient,usetechnologytofindthearea.

a. Totheleftofz=-1.95b. Totherightofz=-0.57c. Betweenz=-1.55andz=1.04�d. P(z>1.28)�e. P(-2.15<z<1.55)�