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ThepharmacistatArnoldPalmerHospital,WendeHuehnBrown,receives12requests forprescriptionseachhour,Poissondistributed.Itakesherameantimeof4minutesto fileach,folowinganegativeexponentialdistribution. a. Whatistheaveragenumberofprescriptionsinthequeue? [",",","] b. Howlongwiltheaverageprescriptionspendinthequeue? [",",","] minutes c. Wendedecidestohireasecondpharmacist,AjayAgerwal,withwhom shewent toscho landwhooperatesathesamespe dinfilingprescriptions.Howwilthe answerstoparts(a)and(b)change?(a)= [",",","] ,(b)= [",",","] minutes Answer1: 3.2 Answer2: 16 Answer3: .152 Answer4: .76 ThetypicalsubwaystationinWashington,DC,hassixturnstiles,eachofwhichcanbe controledbythestationmanagertobeusedforeitherentranceorexitcontrol—but neverforboth.Themanagermustdecideatdifferentimesofthedayhowmany turnstilestouseforenteringpassengersandhowmanytouseforexitingpassengers. AtheGeorgeWashingtonUniversity(GWU)rateofabout84perminutebetwe 9a.m.Passengersexiting trainsathestopreachtheexiturnstileareaatarateofabout48perminuteduringthe samemorningrushhours.Eachturnstilecanalowanaverageof30passengersper minutetoenterorexit.Arrivalandservicetimeshavebe nthoughtofolowPoisson andnegativeexponentialdistributions,respectively.Assumeridersform acommon queueatbothentryandexiturnstileareasandproce dtothefirstemptyturnstile. TheGWUstationmanager,GeraldAase,doesnotwantheaveragepas engerat hisstationtohavetowaitinaturnstilelineformorethan6seconds,nordoeshe wantmorethan8peopleinanyqueueatanyaveragetime. Howmanyturnstilesshouldbeopenedineachdirectioneverymorning? a.Entering= [",",","] b.Exiting= [",",","] Answer1: 4 Answer2: 2 TedGlickman,theadministratoratD.C.GeneralHospitalemergencyro m,facesthe problem ofprovidingtreatmentforpatientswhoarriveatdifferentratesduringtheday. Therearefourdoctorsavailabletotreatpatientswhenne ded.Ifnotne ded,theycan beassignedotheresponsibilities(suchasdoinglabtests,reports,Xraydiagnoses)or elserescheduledtoworkatotherhours. Itisimportantoprovidequickandresponsivetreatment,andTedthinksthat,onthe average,patientsshouldnothavetositinthewaitingareaformorethan5 minutesbeforebeingse nbyadoctor.Patientsaretreatedonafirst-come,firstserved basisandse thefirstavailabledoctorafterwaitinginthequeue.Thearrivalpaternfor atypicaldayisasfolows:ArrivalsfolowaPoissondistribution,andtreatmentimes,12minutesontheaverage, folowthenegativeexponentialpatern. Howmanydoctorsshouldbeondutyduringeachperiodtomaintainthelevelofpatient careexpected? a.Betwe n9:0 AM -3:0 PM = [",",","] Doctors b.Betwe n3:0 PM -8:0 PM = [",",","] Doctors c.Betwe n8:0 PM -Midnight=4Doctors Answer1: 3 Answer2: 2 Answer3: 4 RenukaJain’sCarWashtakesaconstantimeof4.5minutesinitsautomatedcarwash cycle.AutosarrivefolowingaPoissondistributionatherateof10perhour.Renuka wantstoknow: a.Theaveragewaitingtimeinline. [",",","] minutes