AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
Solution_Manual_for_Applied_Stat
CHAPTERn2
Sectionn2-1
ProvidenanreasonablendescriptionnofnthensamplenspacenforneachnofnthenrandomnexperimentsninnExercisesn2-1nton2-
17.nTherencannbenmorenthannonenacceptableninterpretationnofneachnexperiment.nDescribenanynassumptionsnyounmake.
2-1. Eachnofnthreenmachinednpartsnisnclassifiednasneithernabovenornbelownthentargetnspecificationnfornthenpart.nLetn anandnb
denotenanpartnabovenandnbelownthenspecification,nrespectively.
S aaan,naabn,naban,nabbn,nbaan,nbabn,nbban,nbbb
2-2. Eachnofnfourntransmittednbitsnisnclassifiednasneitherninnerrornornnotninnerror.
Letnenandnondenotenanbitninnerrornandnnotninnerrorn(ondenotesnokay),nrespectively.
eeeeneeeon,n,neoeeneoeon,n,noeeenoeeon,n,nooeen ooeon,,
S
eeoen,neooen,noeoen,noooen,
eeoon,neooon,noeoon,noooo
2-3.
Innthenfinalninspectionnofnelectronicnpowernsupplies,neithernunitsnpass,nornthreentypesnofnnonconformitiesnmightno
ccur:nfunctional,nminor,norncosmetic.nThreenunitsnareninspected.
Letnandenotenannacceptablenpowernsupply.
Letnf,nm,nandncndenotenanpowernsupplynthatnhasnanfunctional,nminor,norncosmeticnerror,nrespectively.n
Snan,nfn,nmn,nc
2-4. Thennumbernofnhitsn(views)nisnrecordednatnanhigh-volumenWebnsiteninnanday.
S 0,1,2,... =nsetnofnnonnegativenintegers
2-5. Eachnofn24nWebnsitesnisnclassifiednasncontainingnornnotncontainingnbannernads.
Letnynandnnndenotenanwebnsitenthatncontainsnandndoesnnotncontainnbannernads.
Thensamplenspacenisnthensetnofnallnpossiblensequencesnofnynandnnnofnlengthn24.nAnnexamplenoutcomeninnthensamplenspacenis
2-1
,AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
S yynnynyyynnnynynnnnyynnnyy
2-6. Annammeternthatndisplaysnthreendigitsnisnusedntonmeasurencurrentninnmilliamperes.
Anvectornwithnthreencomponentsncanndescribenthenthreendigitsnofnthenammeter.nEachndigitncannben0,1,2,...,
9.nThensamplenspacenSnisn1000npossiblenthreendigitnintegers,nS 000n,001n,...,n999
2-7. Anscalenthatndisplaysntwondecimalnplacesnisnusedntonmeasurenmaterialnfeedsninnanchemicalnplantninntons.
Snisnthensamplenspacenofn100npossiblentwondigitnintegers.
2-
8.nThenfollowingntwonquestionsnappearnonnannemployeensurveynquestionnaire.nEachnanswernisnchosennfromnthenfivenp
ointnscalen1n(never),n2,n3,n4,n5n(always).
Isnthencorporationnwillingntonlistenntonandnfairlynevaluatennewnideas?nH
ownoftennarenmyncoworkersnimportantninnmynoverallnjobnperformance?
Letnannorderednpairnofnnumbers,nsuchnasn43ndenotenthenresponsenonnthenfirstnandnsecondnquestion.nThen,nSnconsist
snofnthen25norderednpairsn 1n1,12,n.n.n.n,55
2-9. Thenconcentrationnofnozonentonthennearestnpartnpernbillion.
S 0n,1,2,...,1En09 innppb.
2-10. Thentimenuntilnanservicentransactionnisnrequestednofnancomputerntonthennearestnmillisecond.
S 0n,1,2n,..., innmilliseconds
2-11. ThenpHnreadingnofnanwaternsamplentonthennearestntenthnofnanunit.
S 1n.0n,1n.1,1n.2n,nn14n.0
2-12.
Thenvoidsninnanferritenslabnarenclassifiednasnsmall,nmedium,nornlarge.nThennumbernofnvoidsninneachncategor
ynisnmeasurednbynannopticalninspectionnofnansample.
Letns,nm,nandnlndenotensmall,nmedium,nandnlarge,nrespectively.nThennSn=n{s,nm,nl,nss,nsm,nsl,n….
}n2-13 Thentimenofnanchemicalnreactionnisnrecordedntonthennearestnmillisecond.
S 0n,1,2n,..., innmilliseconds.
2-
14.nAnnordernfornannautomobilencannspecifyneithernannautomaticnornanstandardntransmission,neithernwithnornwithoutnair
nconditioning,nandnwithnanynonenofnthenfourncolorsnred,nblue,nblack,nornwhite.nDescribenthensetnofnpossiblenordersnfornth
isnexperiment.
2-2
,AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
automatic standard
ntransmission
ntransmissio
n
with with without
nair without nair nair
nair
rednbluenblacknnnn white rednbluenblack whitennnnnn rednbluenblack white rednbluenblack white
2-15.nAnsampledninjection-
moldednpartncouldnhavenbeennproducedninneithernonenofntwonpressesnandninnanynonenofntheneightncavitiesninneachnpress.
PnRESn 1
S 2
Cn AVITY
1n n 2n n 3 4 5 6nnnn 7nnnnn 8 1 2 3 4 5 6 7 8
2-16.
Annordernfornancomputernsystemncannspecifynmemorynofn4,n8,norn12ngigabytesnandndisknstoragenofn200,n300,norn
400ngigabytes.nDescribenthensetnofnpossiblenorders.
memory
4 8 12
disknstorage
200 300 400 200 300 400 200 300 400
2-17. Callsnarenrepeatedlynplacedntonanbusynphonenlinenuntilnanconnectionnisnachieved.
Letncnandnbndenotenconnectnandnbusy,nrespectively.nThennSn=n{c,nbc,nbbc,nbbbc,nbbbbc,n…}
2-18.
Threenattemptsnarenmadentonreadndataninnanmagneticnstoragendevicenbeforenannerrornrecoverynprocedurenthatnrepositi
onsnthenmagneticnheadnisnused.nThenerrornrecoverynprocedurenattemptsnthreenrepositioningsnbeforenann“abort’’nmessag
enisnsentntonthenoperator.nLet
sndenotenthensuccessnofnanreadnoperationnf
denotenthenfailurenofnanreadnoperation
2-3
, AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
Sndenotenthensuccessnofnannerrornrecoverynprocedur
enFndenotenthenfailurenofnannerrornrecoverynprocedur
enAndenotenannabortnmessagensentntonthenoperator
Describenthensamplenspacenofnthisnexperimentnwithnantreendiagram.
S sn, fsn,nffsn,nfffSn,nfffFSn,nfffFFSn,nfffFFFA
2-19. ThreeneventsnarenshownnonnthenVennndiagramninnthenfollowingnfigure:
Reproducenthenfigurenandnshadenthenregionnthatncorrespondsntoneachnofnthenfollowingnevents.
(a)nA nnnnn (b)nA B A B C (d) B C (e) A B C
(c)n(a)
(b)
(c)
2-4
Solution_Manual_for_Applied_Stat
CHAPTERn2
Sectionn2-1
ProvidenanreasonablendescriptionnofnthensamplenspacenforneachnofnthenrandomnexperimentsninnExercisesn2-1nton2-
17.nTherencannbenmorenthannonenacceptableninterpretationnofneachnexperiment.nDescribenanynassumptionsnyounmake.
2-1. Eachnofnthreenmachinednpartsnisnclassifiednasneithernabovenornbelownthentargetnspecificationnfornthenpart.nLetn anandnb
denotenanpartnabovenandnbelownthenspecification,nrespectively.
S aaan,naabn,naban,nabbn,nbaan,nbabn,nbban,nbbb
2-2. Eachnofnfourntransmittednbitsnisnclassifiednasneitherninnerrornornnotninnerror.
Letnenandnondenotenanbitninnerrornandnnotninnerrorn(ondenotesnokay),nrespectively.
eeeeneeeon,n,neoeeneoeon,n,noeeenoeeon,n,nooeen ooeon,,
S
eeoen,neooen,noeoen,noooen,
eeoon,neooon,noeoon,noooo
2-3.
Innthenfinalninspectionnofnelectronicnpowernsupplies,neithernunitsnpass,nornthreentypesnofnnonconformitiesnmightno
ccur:nfunctional,nminor,norncosmetic.nThreenunitsnareninspected.
Letnandenotenannacceptablenpowernsupply.
Letnf,nm,nandncndenotenanpowernsupplynthatnhasnanfunctional,nminor,norncosmeticnerror,nrespectively.n
Snan,nfn,nmn,nc
2-4. Thennumbernofnhitsn(views)nisnrecordednatnanhigh-volumenWebnsiteninnanday.
S 0,1,2,... =nsetnofnnonnegativenintegers
2-5. Eachnofn24nWebnsitesnisnclassifiednasncontainingnornnotncontainingnbannernads.
Letnynandnnndenotenanwebnsitenthatncontainsnandndoesnnotncontainnbannernads.
Thensamplenspacenisnthensetnofnallnpossiblensequencesnofnynandnnnofnlengthn24.nAnnexamplenoutcomeninnthensamplenspacenis
2-1
,AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
S yynnynyyynnnynynnnnyynnnyy
2-6. Annammeternthatndisplaysnthreendigitsnisnusedntonmeasurencurrentninnmilliamperes.
Anvectornwithnthreencomponentsncanndescribenthenthreendigitsnofnthenammeter.nEachndigitncannben0,1,2,...,
9.nThensamplenspacenSnisn1000npossiblenthreendigitnintegers,nS 000n,001n,...,n999
2-7. Anscalenthatndisplaysntwondecimalnplacesnisnusedntonmeasurenmaterialnfeedsninnanchemicalnplantninntons.
Snisnthensamplenspacenofn100npossiblentwondigitnintegers.
2-
8.nThenfollowingntwonquestionsnappearnonnannemployeensurveynquestionnaire.nEachnanswernisnchosennfromnthenfivenp
ointnscalen1n(never),n2,n3,n4,n5n(always).
Isnthencorporationnwillingntonlistenntonandnfairlynevaluatennewnideas?nH
ownoftennarenmyncoworkersnimportantninnmynoverallnjobnperformance?
Letnannorderednpairnofnnumbers,nsuchnasn43ndenotenthenresponsenonnthenfirstnandnsecondnquestion.nThen,nSnconsist
snofnthen25norderednpairsn 1n1,12,n.n.n.n,55
2-9. Thenconcentrationnofnozonentonthennearestnpartnpernbillion.
S 0n,1,2,...,1En09 innppb.
2-10. Thentimenuntilnanservicentransactionnisnrequestednofnancomputerntonthennearestnmillisecond.
S 0n,1,2n,..., innmilliseconds
2-11. ThenpHnreadingnofnanwaternsamplentonthennearestntenthnofnanunit.
S 1n.0n,1n.1,1n.2n,nn14n.0
2-12.
Thenvoidsninnanferritenslabnarenclassifiednasnsmall,nmedium,nornlarge.nThennumbernofnvoidsninneachncategor
ynisnmeasurednbynannopticalninspectionnofnansample.
Letns,nm,nandnlndenotensmall,nmedium,nandnlarge,nrespectively.nThennSn=n{s,nm,nl,nss,nsm,nsl,n….
}n2-13 Thentimenofnanchemicalnreactionnisnrecordedntonthennearestnmillisecond.
S 0n,1,2n,..., innmilliseconds.
2-
14.nAnnordernfornannautomobilencannspecifyneithernannautomaticnornanstandardntransmission,neithernwithnornwithoutnair
nconditioning,nandnwithnanynonenofnthenfourncolorsnred,nblue,nblack,nornwhite.nDescribenthensetnofnpossiblenordersnfornth
isnexperiment.
2-2
,AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
automatic standard
ntransmission
ntransmissio
n
with with without
nair without nair nair
nair
rednbluenblacknnnn white rednbluenblack whitennnnnn rednbluenblack white rednbluenblack white
2-15.nAnsampledninjection-
moldednpartncouldnhavenbeennproducedninneithernonenofntwonpressesnandninnanynonenofntheneightncavitiesninneachnpress.
PnRESn 1
S 2
Cn AVITY
1n n 2n n 3 4 5 6nnnn 7nnnnn 8 1 2 3 4 5 6 7 8
2-16.
Annordernfornancomputernsystemncannspecifynmemorynofn4,n8,norn12ngigabytesnandndisknstoragenofn200,n300,norn
400ngigabytes.nDescribenthensetnofnpossiblenorders.
memory
4 8 12
disknstorage
200 300 400 200 300 400 200 300 400
2-17. Callsnarenrepeatedlynplacedntonanbusynphonenlinenuntilnanconnectionnisnachieved.
Letncnandnbndenotenconnectnandnbusy,nrespectively.nThennSn=n{c,nbc,nbbc,nbbbc,nbbbbc,n…}
2-18.
Threenattemptsnarenmadentonreadndataninnanmagneticnstoragendevicenbeforenannerrornrecoverynprocedurenthatnrepositi
onsnthenmagneticnheadnisnused.nThenerrornrecoverynprocedurenattemptsnthreenrepositioningsnbeforenann“abort’’nmessag
enisnsentntonthenoperator.nLet
sndenotenthensuccessnofnanreadnoperationnf
denotenthenfailurenofnanreadnoperation
2-3
, AppliednStatisticsnandnProbabilitynfornEngineers,n5thnedition
Sndenotenthensuccessnofnannerrornrecoverynprocedur
enFndenotenthenfailurenofnannerrornrecoverynprocedur
enAndenotenannabortnmessagensentntonthenoperator
Describenthensamplenspacenofnthisnexperimentnwithnantreendiagram.
S sn, fsn,nffsn,nfffSn,nfffFSn,nfffFFSn,nfffFFFA
2-19. ThreeneventsnarenshownnonnthenVennndiagramninnthenfollowingnfigure:
Reproducenthenfigurenandnshadenthenregionnthatncorrespondsntoneachnofnthenfollowingnevents.
(a)nA nnnnn (b)nA B A B C (d) B C (e) A B C
(c)n(a)
(b)
(c)
2-4
