Applied Probability and Statistics C955 Questions and Answers 2025

Applied Probability and Statistics C955
Questions and Answers 2025
ChangingAImproperAFractionsAandAMixedANumbersA-ACORRECTAANSWERS-
ImproperAfractionsAcanAbeAconvertedAtoAmixedAnumbersAbyAfollowingAtheseAsteps:

WriteAdivisionAproblemAwithAnumeratorAdividedAbyAdenominator.

DivideAtoAdetermineAquotientAandAremainder.

WriteAmixedAnumberAwithAtheAquotientAasAtheAwholeAnumberAandAtheAremainderAasAtheAnu
meratorAoverAtheAsameAdenominator.
ChangingAMixedANumbersAIntoAImproperAFractionsA-ACORRECTAANSWERS-
MixedAnumbersAcanAalsoAbeAconvertedAtoAimproperAfractionsAbyAfollowingAtheseAsteps:

MultiplyAtheAwholeAnumberAbyAtheAdenominatorAofAtheAfraction.

ToAtheAproductAgivenAbyAstepA1,AaddAtheAnumberAofAtheAnumerator.

WriteAtheAresultAofAstepA2AasAtheAnumeratorAofAtheAimproperAfraction.ATheAdenominatorAofA
theAimproperAfractionAshouldAbeAtheAdenominatorAofAtheAoriginalAfraction.

SimplifyAtheAimproperAfractionAbyAdivingAtheAnumeratorAandAdenominatorAbyAallAcommonAf
actors.
DiscreteADataA-ACORRECTAANSWERS-
HasAdistinctAvalues,AcanAbeAcounted,AhasAunconnectedApointsA(dots)
ContinuousAdataA-ACORRECTAANSWERS-
HasAvaluesAwithinAaArange,AmeasuredA(notAcounted)AdoesAnotAhaveAgapsAbetweenAdataAp
oints.A(connectedAlinesAorAcurves)
SignAruleAforAMultiplicationAandAdivisionA-ACORRECTAANSWERS-1.A+#AxA+#A=A+#
2.A-#AxA-#A=A+#
AAproductAorAdivisionAofAtwoAnumbersAofAtheAsameAsignAwillAresultAinAaApositiveAnumber
3.A-#AxA+#A=A-#
4.A+#AxA-#A=A-#
AAproductAorAdivisionAofAtwoAnumbersAofAdifferentAsignsAwillAresultAinAaAnegativeAnumber
PrimeANumberA-ACORRECTAANSWERS-
AAprimeAnumberAisAaAnumberAthatAhasAexactlyAtwoApositiveAfactors;A1AandAitself.
CompositeANumberA-ACORRECTAANSWERS-
AAnumberAthatAisAnotAprime.AItAhasA2AorAmoreApositiveAfactor,AincludingA1AandAitself.
PrimeAFactorizationA-ACORRECTAANSWERS-
WritingAtheAnumberAasAaAproductAofAonlyAprimeAnumbers.
GreatestACommonAFactorA(GCF)A-ACORRECTAANSWERS-
TheAlargesAnumberAthatAdividesAallAtheAgivenAnumbersAevenly.

, MultiplesAofAaAnumberA-ACORRECTAANSWERS-
NumbersAthatAcanAbeAobtainedAbyAmultiplyingAtheAgivenAnumberAbyA1,A2,A3,A4,Aetc.
LeastACommonAMultipleA(LCM)A-ACORRECTAANSWERS-
theAsmallestApositiveAnumberAthatAcanAbeAdividedAbyAtheAgivenAnumbers
Centigrade/FahrenheitAConversionsA-ACORRECTAANSWERS-CA=A(FA-A32)AXA5/9
FA=A(CAXA9/5)A+A32
UnitAConversionsAforAHouseholdAMeasuresAofAVolumeA-ACORRECTAANSWERS-
1AtablespoonA=A3Ateaspoons
1AozA=A2Atablespoons
1AcupA=A8Aoz
1ApintA=A2Acups
1AquartA=A1Apints
1AgallonA=A4Aquarts
CommonAMetricAConversionsA-ACORRECTAANSWERS-1ALA=A1000AmL
1kgA=A1000Ag
1AgA=A1000Amg
1AmgA=A1000Amcg
ConversionsAbetweenAHouseholdAandAMetricAUnitsA-ACORRECTAANSWERS-
1AccA(CubicACentimeter)A=A1AmL
1AozA=A30AmL
1ALA=A1.057Aqt
1AtspA=A5AmL
1AkgA=A2.2Albs
1AozA=A28.35Ag
LikeATermsA-ACORRECTAANSWERS-
TermsAthatAhaveAtheAsameAvariableAraisedAtoAtheAsameApower;AtheyAcanAbeAcombinedAusi
ngAadditionAandAsubtraction
Addition/SubtractionAPrincipleA-ACORRECTAANSWERS-
WeAcanAaddAorAsubtractAtheAsameAnumberAtoAbothAsidesAofAanAequationAandAtheAresultingA
expressionAremainsAequal.
Multiplication/DivisionAPrincipleA-ACORRECTAANSWERS-
WeAcanAmultiplyAorAdivideAtheAsameAnumberAtoAbothAsidesAofAanAequationAandAtheAresultin
gAexpressionAremainsAequal.A(DivideAbyA0AisAnotAallowed)
ButterflyAMethodA-ACORRECTAANSWERS-CrossAMultiply,AifAa/bA=Ac/dAthenAaAxAdA=AbAxAc
Slope-InterceptAEquationA-ACORRECTAANSWERS-yA=AmxA+AbA
WhereA"m"AisAtheAslope,A"b"AisAtheAy-
intercept,AandA"x"AandA"y"AfollowAtheAcoordinateAformulaA(x,y)
SlopeAofAaAlineA-ACORRECTAANSWERS-
TheAslopeAofAaAlineAisAtheAratioAofAtheAverticalAchangeAbetweenAtwoApointsAonAtheAlineAtoAth
eAhorizontalAchangeAbetweenAthoseAtwoApoints.
rise:A(y2A-Ay1)A/Arun:A(x2A-Ax1)
ReducingAFractionsAUsingAPrimeAFactorizationA-ACORRECTAANSWERS-
TheAstepsAtoAreduceAaAfractionAthroughAprimeAfactorizationAareAasAfollows:

ListAtheAprimeAfactorsAofAbothAtheAnumeratorAandAdenominator.
CancelAtheAfactorsAthatAareAcommonAtoAbothAtheAnumeratorAandAdenominator.