NormalProbabilities
If you weretold by the postalservicethat you will receivethe packagethat you havebeenwaitingfor
sometimetomorrow, whatis the probabilitythat you will receiveit sometimebetween3:00 PM and 5:00 PM
if you knowthat the postalservice’s hoursof operationsare between7:00 AM to 6:00 PM?
If the hoursof operationsare between7 AM to 6 PM, this meansthey operatefor a total of 11 hours.The
intervalbetween3 PM and 5 PM is 2 hours,and thus the probabilitythat your packagewill arriveis
So thereis a probabilityof that the postalservicewill deliveryour packagesometimebetweenthe
hoursof 3 PM and 5 PM (or duringany 2-hourinterval).That is easyenough.However, mathematically, the
situationis not that simple.The 11-hourintervaland the 2-hourintervalcontainan infinitenumberof times.
So how can one infinityover anotherinfinityproducea probabilityof? To resolvethis issue,we
representthe total probabilityof the 11-hourintervalas a rectangleof area (Figure25). Lookingat the 2-
hour interval,we can see that it is equalto of the total rectangulararea This is why it is convenient
to representprobabilitiesas areas.But sinceareascan be definedby definiteintegrals,we can also define
the probabilityassociatedwith an interval by the definiteintegral