chap06-TIF-BSAFC5

162TheNormalDistributionCHAPTER6:THENORMALDISTRIBUTION1.Initsstandardizedform,thenormaldistributiona)hasameanof0andastandarddeviationof1.b)hasameanof1andavarianceof0.c)hasanareaequalto0.5.d)cannotbeusedtoapproximatediscreteprobabilitydistributions.ANSWER:aTYPE:MCDIFFICULTY:EasyKEYWORDS:standardizednormaldistribution,properties2.Whichofthefollowingaboutthenormaldistributionisnottrue?a)Theoretically,themean,median,andmodearethesame.b)About2/3oftheobservationsfallwithin±1standarddeviationfromthemean.c)Itisadiscreteprobabilitydistribution.d)Itsparametersarethemean,µ,andstandarddeviation,σ.ANSWER:cTYPE:MCDIFFICULTY:EasyKEYWORDS:normaldistribution,properties3.Ifaparticularbatchofdataisapproximatelynormallydistributed,wewouldfindthatapproximatelya)2ofevery3observationswouldfallbetween±1standarddeviationaroundthemean.b)4ofevery5observationswouldfallbetween±1.28standarddeviationsaroundthemean.c)19ofevery20observationswouldfallbetween±2standarddeviationsaroundthemean.d)Alltheabove.ANSWER:dTYPE:MCDIFFICULTY:EasyKEYWORDS:normaldistribution,properties4.ForsomepositivevalueofZ,theprobabilitythatastandardnormalvariableisbetween0andZis0.3770.ThevalueofZisa)0.18b)0.81c)1.16d)1.47ANSWER:cTYPE:MCDIFFICULTY:ModerateKEYWORDS:standardizednormaldistribution,value5.ForsomevalueofZ,theprobabilitythatastandardnormalvariableisbelowZis0.2090.ThevalueofZisCopyright©2010PearsonEducation,Inc.PublishingasPrenticeHallTheNormalDistribution163a)–0.81b)–0.31c)0.31d)1.96ANSWER:aTYPE:MCDIFFICULTY:ModerateKEYWORDS:standardizednormaldistribution,value6.ForsomepositivevalueofZ,theprobabilitythatastandardnormalvariableisbetween0andZis0.3340.ThevalueofZisa)0.07b)0.37c)0.97d)1.06ANSWER:cTYPE:MCDIFFICULTY:ModerateKEYWORDS:standardizednormaldistribution,value7.ForsomepositivevalueofX,theprobabilitythatastandardnormalvariableisbetween0and+2Xis0.1255.ThevalueofXisa)0.99b)0.40c)0.32d)0.16ANSWER:dTYPE:MCDIFFICULTY:DifficultKEYWORDS:normaldistribution,value8.ForsomepositivevalueofX,theprobabilitythatastandardnormalvariableisbetween0and+1.5Xis0.4332.ThevalueofXisa)0.10b)0.50c)1.00d)1.50ANSWER:cTYPE:MCDIFFICULTY:DifficultKEYWORDS:normaldistribution,value9.GiventhatXisanormallydistributedrandomvariablewithameanof50andastandarddeviationof2,findtheprobabilitythatXisbetween47and54.Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHall164TheNormalDistributionANSWER:0.9104TYPE:PRDIFFICULTY:EasyKEYWORDS:normaldistribution,probability10.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Whatproportionoftheplanrecipientswouldreceivepaymentsbeyondage75?ANSWER:0.0228TYPE:PRDIFFICULTY:EasyKEYWORDS:normaldistribution,probability11.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Whatproportionoftheplanrecipientsdiebeforetheyreachthestandardretirementageof65?ANSWER:0.1957usingExcelor0.1949usingTableE.2TYPE:PRDIFFICULTY:ModerateKEYWORDS:normaldistribution,probability12.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Findtheageatwhichpaymentshaveceasedforapproximately86%oftheplanparticipants.ANSWER:71.78yearsoldTYPE:PRDIFFICULTY:DifficultKEYWORDS:normaldistribution,valueCopyright©2010PearsonEducation,Inc.PublishingasPrenticeHallTheNormalDistribution16513.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findtheprobabilitythatarandomlyselectedcollegestudentwillfindaparkingspotinthelibraryparkinglotinlessthan3minutes.a)0.3551b)0.3085c)0.2674d)0.1915ANSWER:bTYPE:MCDIFFICULTY:EasyKEYWORDS:normaldistribution,probability14.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findtheprobabilitythatarandomlyselectedcollegestudentwilltakebetween2and4.5minutestofindaparkingspotinthelibraryparkinglot.a)0.0919b)0.2255c)0.4938d)0.7745ANSWER:dTYPE:MCDIFFICULTY:EasyKEYWORDS:normaldistribution,probability15.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findthepointinthedistributioninwhich75.8%ofthecollegestudentsexceedwhentryingtofindaparkingspotinthelibraryparkinglot.a)2.8minutesb)3.2minutesc)3.4minutesd)4.2minutesANSWER:aTYPE:MCDIFFICULTY:ModerateKEYWORDS:normaldistribution,value16.Theownerof