AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
Solution_Manual_for_Applied_Stat
CHAPTERh2
Sectionh2-1
ProvidehahreasonablehdescriptionhofhthehsamplehspacehforheachhofhthehrandomhexperimentshinhExercisesh2-1htoh2-
17.hTherehcanhbehmorehthanhonehacceptablehinterpretationhofheachhexperiment.hDescribehanyhassumptionshyouhmake.
2-1. Eachhofhthreehmachinedhpartshishclassifiedhasheitherhabovehorhbelowhthehtargethspecificationhforhthehpart.hLeth ahandhb
denotehahparthabovehandhbelowhthehspecification,hrespectively.
S aaah,haabh,habah,habbh,hbaah,hbabh,hbbah,hbbb
2-2. Eachhofhfourhtransmittedhbitshishclassifiedhasheitherhinherrorhorhnothinherror.
Lethehandhohdenotehahbithinherrorhandhnothinherrorh(ohdenoteshokay),hrespectively.
eeeeheeeoh,h,heoeeheoeoh,h,hoeeehoeeoh,h,hooeeh ooeoh,,
S
eeoeh,heooeh,hoeoeh,hoooeh,
eeooh,heoooh,hoeooh,hoooo
2-3.
Inhthehfinalhinspectionhofhelectronichpowerhsupplies,heitherhunitshpass,horhthreehtypeshofhnonconformitieshmightho
ccur:hfunctional,hminor,horhcosmetic.hThreehunitsharehinspected.
Lethahdenotehanhacceptablehpowerhsupply.
Lethf,hm,handhchdenotehahpowerhsupplyhthathhashahfunctional,hminor,horhcosmeticherror,hrespectively.h
Shah,hfh,hmh,hc
2-4. Thehnumberhofhhitsh(views)hishrecordedhathahhigh-volumehWebhsitehinhahday.
S 0,1,2,... =hsethofhnonnegativehintegers
2-5. Eachhofh24hWebhsiteshishclassifiedhashcontaininghorhnothcontaininghbannerhads.
Lethyhandhnhdenotehahwebhsitehthathcontainshandhdoeshnothcontainhbannerhads.
Thehsamplehspacehishthehsethofhallhpossiblehsequenceshofhyhandhnhofhlengthh24.hAnhexamplehoutcomehinhthehsamplehspacehis
2-1
,AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
S yynnynyyynhnynynnnnyyhnnyy
2-6. Anhammeterhthathdisplayshthreehdigitshishusedhtohmeasurehcurrenthinhmilliamperes.
Ahvectorhwithhthreehcomponentshcanhdescribehthehthreehdigitshofhthehammeter.hEachhdigithcanhbeh0,1,2,...,
9.hThehsamplehspacehShish1000hpossiblehthreehdigithintegers,hS 000h,001h,...,h999
2-7. Ahscalehthathdisplayshtwohdecimalhplaceshishusedhtohmeasurehmaterialhfeedshinhahchemicalhplanthinhtons.
Shishthehsamplehspacehofh100hpossiblehtwohdigithintegers.
2-
8.hThehfollowinghtwohquestionshappearhonhanhemployeehsurveyhquestionnaire.hEachhanswerhishchosenhfromhthehfivehp
ointhscaleh1h(never),h2,h3,h4,h5h(always).
Ishthehcorporationhwillinghtohlistenhtohandhfairlyhevaluatehnewhideas?hH
owhoftenharehmyhcoworkershimportanthinhmyhoverallhjobhperformance?
Lethanhorderedhpairhofhnumbers,hsuchhash43hdenotehthehresponsehonhthehfirsthandhsecondhquestion.hThen,hShconsist
shofhtheh25horderedhpairsh 1h1,12,h.h.h.h,55
2-9. Thehconcentrationhofhozonehtohthehnearesthparthperhbillion.
S 0h,1,2,...,1Eh09 inhppb.
2-10. Thehtimehuntilhahservicehtransactionhishrequestedhofhahcomputerhtohthehnearesthmillisecond.
S 0h,1,2h,..., inhmilliseconds
2-11. ThehpHhreadinghofhahwaterhsamplehtohthehnearesthtenthhofhahunit.
S 1h.0h,1h.1,1h.2h,hh14h.0
2-12.
Thehvoidshinhahferritehslabharehclassifiedhashsmall,hmedium,horhlarge.hThehnumberhofhvoidshinheachhcategor
yhishmeasuredhbyhanhopticalhinspectionhofhahsample.
Leths,hm,handhlhdenotehsmall,hmedium,handhlarge,hrespectively.hThenhSh=h{s,hm,hl,hss,hsm,hsl,h….
}h2-13 Thehtimehofhahchemicalhreactionhishrecordedhtohthehnearesthmillisecond.
S 0h,1,2h,..., inhmilliseconds.
2-
14.hAnhorderhforhanhautomobilehcanhspecifyheitherhanhautomatichorhahstandardhtransmission,heitherhwithhorhwithouthair
hconditioning,handhwithhanyhonehofhthehfourhcolorshred,hblue,hblack,horhwhite.hDescribehthehsethofhpossiblehordershforhth
ishexperiment.
2-2
,AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
automatic standard
htransmission
htransmissio
n
with with without
hair without hair hair
hair
redhbluehblackhhhh white redhbluehblack whitehhhhhh redhbluehblack white redhbluehblack white
2-15.hAhsampledhinjection-
moldedhparthcouldhhavehbeenhproducedhinheitherhonehofhtwohpresseshandhinhanyhonehofhtheheighthcavitieshinheachhpress.
PhRESh 1
S 2
Ch AVITY
1h h 2h h 3 4 5 6hhhh 7hhhhh 8 1 2 3 4 5 6 7 8
2-16.
Anhorderhforhahcomputerhsystemhcanhspecifyhmemoryhofh4,h8,horh12hgigabyteshandhdiskhstoragehofh200,h300,horh
400hgigabytes.hDescribehthehsethofhpossiblehorders.
memory
4 8 12
diskhstorage
200 300 400 200 300 400 200 300 400
2-17. Callsharehrepeatedlyhplacedhtohahbusyhphonehlinehuntilhahconnectionhishachieved.
Lethchandhbhdenotehconnecthandhbusy,hrespectively.hThenhSh=h{c,hbc,hbbc,hbbbc,hbbbbc,h…}
2-18.
Threehattemptsharehmadehtohreadhdatahinhahmagnetichstoragehdevicehbeforehanherrorhrecoveryhprocedurehthathrepositi
onshthehmagnetichheadhishused.hTheherrorhrecoveryhprocedurehattemptshthreehrepositioningshbeforehanh“abort’’hmessag
ehishsenthtohthehoperator.hLet
shdenotehthehsuccesshofhahreadhoperationhf
denotehthehfailurehofhahreadhoperation
2-3
, AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
Shdenotehthehsuccesshofhanherrorhrecoveryhprocedur
ehFhdenotehthehfailurehofhanherrorhrecoveryhprocedur
ehAhdenotehanhaborthmessagehsenthtohthehoperator
Describehthehsamplehspacehofhthishexperimenthwithhahtreehdiagram.
S sh, fsh,hffsh,hfffSh,hfffFSh,hfffFFSh,hfffFFFA
2-19. ThreeheventsharehshownhonhthehVennhdiagramhinhthehfollowinghfigure:
Reproducehthehfigurehandhshadehthehregionhthathcorrespondshtoheachhofhthehfollowinghevents.
(a)hA hhhhh (b)hA B A B C (d) B C (e) A B C
(c)h(a)
(b)
(c)
2-4
Solution_Manual_for_Applied_Stat
CHAPTERh2
Sectionh2-1
ProvidehahreasonablehdescriptionhofhthehsamplehspacehforheachhofhthehrandomhexperimentshinhExercisesh2-1htoh2-
17.hTherehcanhbehmorehthanhonehacceptablehinterpretationhofheachhexperiment.hDescribehanyhassumptionshyouhmake.
2-1. Eachhofhthreehmachinedhpartshishclassifiedhasheitherhabovehorhbelowhthehtargethspecificationhforhthehpart.hLeth ahandhb
denotehahparthabovehandhbelowhthehspecification,hrespectively.
S aaah,haabh,habah,habbh,hbaah,hbabh,hbbah,hbbb
2-2. Eachhofhfourhtransmittedhbitshishclassifiedhasheitherhinherrorhorhnothinherror.
Lethehandhohdenotehahbithinherrorhandhnothinherrorh(ohdenoteshokay),hrespectively.
eeeeheeeoh,h,heoeeheoeoh,h,hoeeehoeeoh,h,hooeeh ooeoh,,
S
eeoeh,heooeh,hoeoeh,hoooeh,
eeooh,heoooh,hoeooh,hoooo
2-3.
Inhthehfinalhinspectionhofhelectronichpowerhsupplies,heitherhunitshpass,horhthreehtypeshofhnonconformitieshmightho
ccur:hfunctional,hminor,horhcosmetic.hThreehunitsharehinspected.
Lethahdenotehanhacceptablehpowerhsupply.
Lethf,hm,handhchdenotehahpowerhsupplyhthathhashahfunctional,hminor,horhcosmeticherror,hrespectively.h
Shah,hfh,hmh,hc
2-4. Thehnumberhofhhitsh(views)hishrecordedhathahhigh-volumehWebhsitehinhahday.
S 0,1,2,... =hsethofhnonnegativehintegers
2-5. Eachhofh24hWebhsiteshishclassifiedhashcontaininghorhnothcontaininghbannerhads.
Lethyhandhnhdenotehahwebhsitehthathcontainshandhdoeshnothcontainhbannerhads.
Thehsamplehspacehishthehsethofhallhpossiblehsequenceshofhyhandhnhofhlengthh24.hAnhexamplehoutcomehinhthehsamplehspacehis
2-1
,AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
S yynnynyyynhnynynnnnyyhnnyy
2-6. Anhammeterhthathdisplayshthreehdigitshishusedhtohmeasurehcurrenthinhmilliamperes.
Ahvectorhwithhthreehcomponentshcanhdescribehthehthreehdigitshofhthehammeter.hEachhdigithcanhbeh0,1,2,...,
9.hThehsamplehspacehShish1000hpossiblehthreehdigithintegers,hS 000h,001h,...,h999
2-7. Ahscalehthathdisplayshtwohdecimalhplaceshishusedhtohmeasurehmaterialhfeedshinhahchemicalhplanthinhtons.
Shishthehsamplehspacehofh100hpossiblehtwohdigithintegers.
2-
8.hThehfollowinghtwohquestionshappearhonhanhemployeehsurveyhquestionnaire.hEachhanswerhishchosenhfromhthehfivehp
ointhscaleh1h(never),h2,h3,h4,h5h(always).
Ishthehcorporationhwillinghtohlistenhtohandhfairlyhevaluatehnewhideas?hH
owhoftenharehmyhcoworkershimportanthinhmyhoverallhjobhperformance?
Lethanhorderedhpairhofhnumbers,hsuchhash43hdenotehthehresponsehonhthehfirsthandhsecondhquestion.hThen,hShconsist
shofhtheh25horderedhpairsh 1h1,12,h.h.h.h,55
2-9. Thehconcentrationhofhozonehtohthehnearesthparthperhbillion.
S 0h,1,2,...,1Eh09 inhppb.
2-10. Thehtimehuntilhahservicehtransactionhishrequestedhofhahcomputerhtohthehnearesthmillisecond.
S 0h,1,2h,..., inhmilliseconds
2-11. ThehpHhreadinghofhahwaterhsamplehtohthehnearesthtenthhofhahunit.
S 1h.0h,1h.1,1h.2h,hh14h.0
2-12.
Thehvoidshinhahferritehslabharehclassifiedhashsmall,hmedium,horhlarge.hThehnumberhofhvoidshinheachhcategor
yhishmeasuredhbyhanhopticalhinspectionhofhahsample.
Leths,hm,handhlhdenotehsmall,hmedium,handhlarge,hrespectively.hThenhSh=h{s,hm,hl,hss,hsm,hsl,h….
}h2-13 Thehtimehofhahchemicalhreactionhishrecordedhtohthehnearesthmillisecond.
S 0h,1,2h,..., inhmilliseconds.
2-
14.hAnhorderhforhanhautomobilehcanhspecifyheitherhanhautomatichorhahstandardhtransmission,heitherhwithhorhwithouthair
hconditioning,handhwithhanyhonehofhthehfourhcolorshred,hblue,hblack,horhwhite.hDescribehthehsethofhpossiblehordershforhth
ishexperiment.
2-2
,AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
automatic standard
htransmission
htransmissio
n
with with without
hair without hair hair
hair
redhbluehblackhhhh white redhbluehblack whitehhhhhh redhbluehblack white redhbluehblack white
2-15.hAhsampledhinjection-
moldedhparthcouldhhavehbeenhproducedhinheitherhonehofhtwohpresseshandhinhanyhonehofhtheheighthcavitieshinheachhpress.
PhRESh 1
S 2
Ch AVITY
1h h 2h h 3 4 5 6hhhh 7hhhhh 8 1 2 3 4 5 6 7 8
2-16.
Anhorderhforhahcomputerhsystemhcanhspecifyhmemoryhofh4,h8,horh12hgigabyteshandhdiskhstoragehofh200,h300,horh
400hgigabytes.hDescribehthehsethofhpossiblehorders.
memory
4 8 12
diskhstorage
200 300 400 200 300 400 200 300 400
2-17. Callsharehrepeatedlyhplacedhtohahbusyhphonehlinehuntilhahconnectionhishachieved.
Lethchandhbhdenotehconnecthandhbusy,hrespectively.hThenhSh=h{c,hbc,hbbc,hbbbc,hbbbbc,h…}
2-18.
Threehattemptsharehmadehtohreadhdatahinhahmagnetichstoragehdevicehbeforehanherrorhrecoveryhprocedurehthathrepositi
onshthehmagnetichheadhishused.hTheherrorhrecoveryhprocedurehattemptshthreehrepositioningshbeforehanh“abort’’hmessag
ehishsenthtohthehoperator.hLet
shdenotehthehsuccesshofhahreadhoperationhf
denotehthehfailurehofhahreadhoperation
2-3
, AppliedhStatisticshandhProbabilityhforhEngineers,h5thhedition
Shdenotehthehsuccesshofhanherrorhrecoveryhprocedur
ehFhdenotehthehfailurehofhanherrorhrecoveryhprocedur
ehAhdenotehanhaborthmessagehsenthtohthehoperator
Describehthehsamplehspacehofhthishexperimenthwithhahtreehdiagram.
S sh, fsh,hffsh,hfffSh,hfffFSh,hfffFFSh,hfffFFFA
2-19. ThreeheventsharehshownhonhthehVennhdiagramhinhthehfollowinghfigure:
Reproducehthehfigurehandhshadehthehregionhthathcorrespondshtoheachhofhthehfollowinghevents.
(a)hA hhhhh (b)hA B A B C (d) B C (e) A B C
(c)h(a)
(b)
(c)
2-4
