AppliedbStatisticsbandbProbabilitybforbEngineers,b5thbedition
CHAPTERb2
Sectionb2-1
ProvidebabreasonablebdescriptionbofbthebsamplebspacebforbeachbofbthebrandombexperimentsbinbExercisesb2-1btob2-
17.bTherebcanbbebmorebthanbonebacceptablebinterpretationbofbeachbexperiment.bDescribebanybassumptionsbyoubmake.
2-1. Eachbofbthreebmachinedbpartsbisbclassifiedbasbeitherbaboveborbbelowbthebtargetbspecificationbforbthebpart.bLetbabandbb
denotebabpartbabovebandbbelowbthebspecification,brespectively.
S aaab,baabb,babab,babbb,bbaab,bbabb,bbbab,bbbbb
2-2. Eachbofbfourbtransmittedbbitsbisbclassifiedbasbeitherbinberrorborbnotbinberror.
Letbebandbobdenotebabbitbinberrorbandbnotbinberrorb(obdenotesbokay),brespectively.
eeeebeeeob,b,beoeebeoeob,b,boeeeboeeob,b,booeeb ooeob,,
S
eeoeb,beooeb,boeoeb,boooeb,
eeoob,beooob,boeoob,boooob
2-3.
Inbthebfinalbinspectionbofbelectronicbpowerbsupplies,beitherbunitsbpass,borbthreebtypesbofbnonconformitiesbmightbocc
ur:bfunctional,bminor,borbcosmetic.bThreebunitsbarebinspected.
Letbabdenotebanbacceptablebpowerbsupply.
Letbf,bm,bandbcbdenotebabpowerbsupplybthatbhasbabfunctional,bminor,borbcosmeticberror,brespectively.b
Sbab,bfb,bmb,bc
2-4. Thebnumberbofbhitsb(views)bisbrecordedbatbabhigh-volumebWebbsitebinbabday.
S 0,1,2,... =bsetbofbnonnegativebintegers
2-5. Eachbofb24bWebbsitesbisbclassifiedbasbcontainingborbnotbcontainingbbannerbads.
Letbybandbnbdenotebabwebbsitebthatbcontainsbandbdoesbnotbcontainbbannerbads.
Thebsamplebspacebisbthebsetbofballbpossiblebsequencesbofbybandbnbofblengthb24.bAnbexampleboutcomebinbthebsamplebspacebis
2-1
,AppliedbStatisticsbandbProbabilitybforbEngineers,b5thbedition
S yynnynyyynbnynynnnnyybnnyyb
2-6. Anbammeterbthatbdisplaysbthreebdigitsbisbusedbtobmeasurebcurrentbinbmilliamperes.
Abvectorbwithbthreebcomponentsbcanbdescribebthebthreebdigitsbofbthebammeter.bEachbdigitbcanbbeb0,1,2,...,9
.bThebsamplebspacebSbisb1000bpossiblebthreebdigitbintegers,bS 000b,001b,...,b999b
2-7. Abscalebthatbdisplaysbtwobdecimalbplacesbisbusedbtobmeasurebmaterialbfeedsbinbabchemicalbplantbinbtons.
Sbisbthebsamplebspacebofb100bpossiblebtwobdigitbintegers.
2-
8.bThebfollowingbtwobquestionsbappearbonbanbemployeebsurveybquestionnaire.bEachbanswerbisbchosenbfrombthebfiveb
pointbscaleb1b(never),b2,b3,b4,b5b(always).
Isbthebcorporationbwillingbtoblistenbtobandbfairlybevaluatebnewbideas?bHo
wboftenbarebmybcoworkersbimportantbinbmyboverallbjobbperformance?
Letbanborderedbpairbofbnumbers,bsuchbasb43bdenotebthebresponsebonbthebfirstbandbsecondbquestion.bThen,bSbconsist
sbofbtheb25borderedbpairsb 1b1,12,b.b.b.b,55
2-9. Thebconcentrationbofbozonebtobthebnearestbpartbperbbillion.
S 0b,1,2,...,1Eb09 inbppb.
2-10. Thebtimebuntilbabservicebtransactionbisbrequestedbofbabcomputerbtobthebnearestbmillisecond.
S 0b,1,2b,..., inbmilliseconds
2-11. ThebpHbreadingbofbabwaterbsamplebtobthebnearestbtenthbofbabunit.
S 1b.0b,1b.1,1b.2b,b…b14b.0
2-12.
Thebvoidsbinbabferritebslabbarebclassifiedbasbsmall,bmedium,borblarge.bThebnumberbofbvoidsbinbeachb
categorybisbmeasuredbbybanbopticalbinspectionbofbabsample.
Letbs,bm,bandblbdenotebsmall,bmedium,bandblarge,brespectively.bThenbSb=b{s,bm,bl,bss,bsm,bsl,b….
}b2-13 Thebtimebofbabchemicalbreactionbisbrecordedbtobthebnearestbmillisecond.
S 0b,1,2b,..., inbmilliseconds.
2-
14.bAnborderbforbanbautomobilebcanbspecifybeitherbanbautomaticborbabstandardbtransmission,beitherbwithborbwithoutbair
bconditioning,bandbwithbanybonebofbthebfourbcolorsbred,bblue,bblack, borbwhite.bDescribebthebsetbofbpossiblebordersbforbth
isbexperiment.
,2-2
, AppliedbStatisticsbandbProbabilitybforbEngineers,b5thbedition
automatic standard
b transmissio
b transmissi
n
on
with with without
b ai without b ai b ai
r b air r r
redbbluebblackb b white redbbluebblack whiteb b redbbluebblack white redbbluebblack white
2-15.bAbsampledbinjection-
moldedbpartbcouldbhavebbeenbproducedbinbeitherbonebofbtwobpressesbandbinbanybonebofbthebeightbcavitiesbinbeachbpress.
PbRESbS 1
2
CbAVIbT
Y
1b b 2b b 3 4 5 6b b 7b b 8 1 2 3 4 5 6 7 8
2-16.
Anborderbforbabcomputerbsystembcanbspecifybmemorybofb4,b8,borb12bgigabytesbandbdiskbstoragebofb200,b
300,borb400bgigabytes.bDescribebthebsetbofbpossibleborders.
memory
4 8 12
diskbstorage
200 300 400 200 300 400 200 300 400
2-17. Callsbarebrepeatedlybplacedbtobabbusybphoneblinebuntilbabconnectionbisbachieved.
Letbcbandbbbdenotebconnectbandbbusy,brespectively.bThenbSb=b{c,bbc,bbbc,bbbbc,bbbbbc,b…}
2-18.
Threebattemptsbarebmadebtobreadbdatabinbabmagneticbstoragebdevicebbeforebanberrorbrecoverybprocedurebthatbreposition
sbthebmagneticbheadbisbused.bTheberrorbrecoverybprocedurebattemptsbthreebrepositioningsbbeforebanb“abort’’bmessageb
isbsentbtobtheboperator.bLet
sbdenotebthebsuccessbofbabreadboperationbf
denotebthebfailurebofbabreadboperation
2-3
CHAPTERb2
Sectionb2-1
ProvidebabreasonablebdescriptionbofbthebsamplebspacebforbeachbofbthebrandombexperimentsbinbExercisesb2-1btob2-
17.bTherebcanbbebmorebthanbonebacceptablebinterpretationbofbeachbexperiment.bDescribebanybassumptionsbyoubmake.
2-1. Eachbofbthreebmachinedbpartsbisbclassifiedbasbeitherbaboveborbbelowbthebtargetbspecificationbforbthebpart.bLetbabandbb
denotebabpartbabovebandbbelowbthebspecification,brespectively.
S aaab,baabb,babab,babbb,bbaab,bbabb,bbbab,bbbbb
2-2. Eachbofbfourbtransmittedbbitsbisbclassifiedbasbeitherbinberrorborbnotbinberror.
Letbebandbobdenotebabbitbinberrorbandbnotbinberrorb(obdenotesbokay),brespectively.
eeeebeeeob,b,beoeebeoeob,b,boeeeboeeob,b,booeeb ooeob,,
S
eeoeb,beooeb,boeoeb,boooeb,
eeoob,beooob,boeoob,boooob
2-3.
Inbthebfinalbinspectionbofbelectronicbpowerbsupplies,beitherbunitsbpass,borbthreebtypesbofbnonconformitiesbmightbocc
ur:bfunctional,bminor,borbcosmetic.bThreebunitsbarebinspected.
Letbabdenotebanbacceptablebpowerbsupply.
Letbf,bm,bandbcbdenotebabpowerbsupplybthatbhasbabfunctional,bminor,borbcosmeticberror,brespectively.b
Sbab,bfb,bmb,bc
2-4. Thebnumberbofbhitsb(views)bisbrecordedbatbabhigh-volumebWebbsitebinbabday.
S 0,1,2,... =bsetbofbnonnegativebintegers
2-5. Eachbofb24bWebbsitesbisbclassifiedbasbcontainingborbnotbcontainingbbannerbads.
Letbybandbnbdenotebabwebbsitebthatbcontainsbandbdoesbnotbcontainbbannerbads.
Thebsamplebspacebisbthebsetbofballbpossiblebsequencesbofbybandbnbofblengthb24.bAnbexampleboutcomebinbthebsamplebspacebis
2-1
,AppliedbStatisticsbandbProbabilitybforbEngineers,b5thbedition
S yynnynyyynbnynynnnnyybnnyyb
2-6. Anbammeterbthatbdisplaysbthreebdigitsbisbusedbtobmeasurebcurrentbinbmilliamperes.
Abvectorbwithbthreebcomponentsbcanbdescribebthebthreebdigitsbofbthebammeter.bEachbdigitbcanbbeb0,1,2,...,9
.bThebsamplebspacebSbisb1000bpossiblebthreebdigitbintegers,bS 000b,001b,...,b999b
2-7. Abscalebthatbdisplaysbtwobdecimalbplacesbisbusedbtobmeasurebmaterialbfeedsbinbabchemicalbplantbinbtons.
Sbisbthebsamplebspacebofb100bpossiblebtwobdigitbintegers.
2-
8.bThebfollowingbtwobquestionsbappearbonbanbemployeebsurveybquestionnaire.bEachbanswerbisbchosenbfrombthebfiveb
pointbscaleb1b(never),b2,b3,b4,b5b(always).
Isbthebcorporationbwillingbtoblistenbtobandbfairlybevaluatebnewbideas?bHo
wboftenbarebmybcoworkersbimportantbinbmyboverallbjobbperformance?
Letbanborderedbpairbofbnumbers,bsuchbasb43bdenotebthebresponsebonbthebfirstbandbsecondbquestion.bThen,bSbconsist
sbofbtheb25borderedbpairsb 1b1,12,b.b.b.b,55
2-9. Thebconcentrationbofbozonebtobthebnearestbpartbperbbillion.
S 0b,1,2,...,1Eb09 inbppb.
2-10. Thebtimebuntilbabservicebtransactionbisbrequestedbofbabcomputerbtobthebnearestbmillisecond.
S 0b,1,2b,..., inbmilliseconds
2-11. ThebpHbreadingbofbabwaterbsamplebtobthebnearestbtenthbofbabunit.
S 1b.0b,1b.1,1b.2b,b…b14b.0
2-12.
Thebvoidsbinbabferritebslabbarebclassifiedbasbsmall,bmedium,borblarge.bThebnumberbofbvoidsbinbeachb
categorybisbmeasuredbbybanbopticalbinspectionbofbabsample.
Letbs,bm,bandblbdenotebsmall,bmedium,bandblarge,brespectively.bThenbSb=b{s,bm,bl,bss,bsm,bsl,b….
}b2-13 Thebtimebofbabchemicalbreactionbisbrecordedbtobthebnearestbmillisecond.
S 0b,1,2b,..., inbmilliseconds.
2-
14.bAnborderbforbanbautomobilebcanbspecifybeitherbanbautomaticborbabstandardbtransmission,beitherbwithborbwithoutbair
bconditioning,bandbwithbanybonebofbthebfourbcolorsbred,bblue,bblack, borbwhite.bDescribebthebsetbofbpossiblebordersbforbth
isbexperiment.
,2-2
, AppliedbStatisticsbandbProbabilitybforbEngineers,b5thbedition
automatic standard
b transmissio
b transmissi
n
on
with with without
b ai without b ai b ai
r b air r r
redbbluebblackb b white redbbluebblack whiteb b redbbluebblack white redbbluebblack white
2-15.bAbsampledbinjection-
moldedbpartbcouldbhavebbeenbproducedbinbeitherbonebofbtwobpressesbandbinbanybonebofbthebeightbcavitiesbinbeachbpress.
PbRESbS 1
2
CbAVIbT
Y
1b b 2b b 3 4 5 6b b 7b b 8 1 2 3 4 5 6 7 8
2-16.
Anborderbforbabcomputerbsystembcanbspecifybmemorybofb4,b8,borb12bgigabytesbandbdiskbstoragebofb200,b
300,borb400bgigabytes.bDescribebthebsetbofbpossibleborders.
memory
4 8 12
diskbstorage
200 300 400 200 300 400 200 300 400
2-17. Callsbarebrepeatedlybplacedbtobabbusybphoneblinebuntilbabconnectionbisbachieved.
Letbcbandbbbdenotebconnectbandbbusy,brespectively.bThenbSb=b{c,bbc,bbbc,bbbbc,bbbbbc,b…}
2-18.
Threebattemptsbarebmadebtobreadbdatabinbabmagneticbstoragebdevicebbeforebanberrorbrecoverybprocedurebthatbreposition
sbthebmagneticbheadbisbused.bTheberrorbrecoverybprocedurebattemptsbthreebrepositioningsbbeforebanb“abort’’bmessageb
isbsentbtobtheboperator.bLet
sbdenotebthebsuccessbofbabreadboperationbf
denotebthebfailurebofbabreadboperation
2-3
