Test Bank For Probability And Statistics For Engineering An
3 3 3 3 3 3 3 3
d The Sciences 8th Ed by Jay L. Devore.
3 3 3 3 3 3 3 3
Chapter313–3Overview3and3Descriptive3Statistics
SHORT3ANSWER
1. Give3one3possible3sample3of3size343from3each3of3the3following3populations:
a. All3daily3newspapers3published3in3the3United3States
b. All3companies3listed3on3the3New3York3Stock3Exchange
c. All3students3at3your3college3or3university
d. All3grade3point3averages3of3students3at3your3college3or3university
ANS:
a. Houston3Chronicle,3Des3Moines3Register,3Chicago3Tribune,3Washington3Post
b. Capital3One,3Campbell3Soup,3Merrill3Lynch,3Pulitzer
c. John3Anderson,3Emily3Black,3Bill3 Carter,3Kay3Davis
d. 2.58.32.96,33.51,33.69
PTS:3 3 1
2. A3Southern3State3University3system3consists3of3233campuses.3An3administrator3wishes3to3make3an3inference3ab
out3the3average3distance3between3the3hometowns3of3students3and3their3campuses.3Describe3and3discuss3several3d
ifferent3sampling3methods3that3might3be3employed.3Would3this3be3an3enumerative3or3an3analytic3study?3Explai
n3your3reasoning.
ANS:
One3could3take3a3simple3random3sample3of3students3from3all3students3in3the3California3State3University3system3a
nd3ask3each3student3in3the3sample3to3report3the3distance3from3their3hometown3to3campus.3Alternatively,3the3sam
ple3could3be3generated3by3taking3a3stratified3random3sample3by3taking3a3simple3random3sample3from3each3of3th
e3233campuses3and3again3asking3each3student3in3the3sample3to3report3the3distance3from3their3hometown3to3camp
us.
Certain3problems3might3arise3with3self3reporting3of3distances,3such3as3recording3error3or3poor3recall.3This3study3is3enu
merative3because3there3exists3a3finite,3identifiable3population3of3objects3from3which3to3sample.
PTS:3 3 1
3. A3Michigan3city3divides3naturally3into3ten3district3neighborhoods.3How3might3a3real3estate3appraiser3select3a3sa
mple3of3single-
family3homes3that3could3be3used3as3a3basis3for3developing3an3equation3to3predict3appraised3value3from3characte
ristics3such3as3age,3size,3number3of3bathrooms,3and3distance3to3the3nearest3school,3and3so3on?3 Is3the3study3enu
merative3or3analytic?
ANS:
One3could3generate3a3simple3random3sample3of3all3single3family3homes3in3the3city3or3a3stratified3random3sample
3by3taking3a3simple3random 3sample3from 3each3of3the3103district 3neighborhoods.3From 3each3of3the3homes3in3the3
sample3the3necessary3variables3would3be3collected.3This3would3be3an3enumerative3study3because3there3exists3a3f
inite,3identifiable3population3of3objects3from3which3to3sample.
, PTS:3 3 1
4. An3experiment3was3carried3out3to3study3how3flow3rate3through3a3solenoid3valve3in3an3automobile’s3pollution-
control3system3depended3on3three3factors:3 armature3lengths,3spring3load,3and3bobbin3depth.3 Two3different3level
s3(low3and3high)3of3each3factor3were3chosen,3and3a3single3observation3on3flow3was3made3for3each3combination3
of3levels.
a. The3resulting3data3set3consisted3of3how3many3observations?
b. Is3this3an3enumerative3or3analytic3study?3Explain3your3reasoning.
ANS:
a. Number3observations3equal3233 233 2=8
b. This3could3be3called3an3analytic3study3because3the3data3would3be3collected3on3an3existing3proc
ess.3There3is3no3sampling3frame.
PTS:3 3 1
5. The3accompanying3data3specific3gravity3values3for3various3wood3types3used3in3construction3.
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct 3a3stem-and-leaf3display3using3repeated3stems3and3comment3on3any3interesting3features3of3the3display.
ANS:
One3method3of3denoting3the3pairs3of3stems3having3equal3values3is3to3denote3the3stem3by3L,3for3‘low’3and3the3se
cond3stem3by3H,3for3‘high’.3 Using3this3notation,3the3stem-and-leaf3display3would3appear3as3follows:
3L 1 stem:3tenths
3H 56678 leaf:3 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The3stem-and-
leaf3display3on3the3previous3page3shows3that3.453is3a3good3representative3value3for3the3data.3 In3addition,3the3dis
play3is3not3symmetric3and3appears3to3be3positively3skewed.3 The3spread3of3the3data3is3.753-
3.313=3.44,3which3is3.44/.453=3.9783or3about 398%3of3the3typical 3value3of3.45.3 This3constitutes 3a3reasonably3large
3amount 3of3variation3in3the3data.3 The3data3value3.753is3a3possible3outlier.
PTS:3 3 1
6. Temperature3transducers3of3a3certain3type3are3shipped3in3batches3of350.3 A3sample3of3603batches3was3selected,
3and3the3number 3of3transducers3in3each3batch3not 3conforming3to3design3specifications 3was3determined,3resulti
ng3in3the3following3data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
43 3 23 3 13 3
3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
13 3 23 3 43 3
0
5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
03 3 23 3 33 3
,2
, a. Determine3frequencies3and3relative3frequencies3for3the3observed3values3of3x3=3number3of
nonconforming3transducers3in3a3batch.
b. What3proportion3of3batches3in3the3sample3has3at3most3four3nonconforming3transducers?3What3proportion3
has3fewer3than3four?3What3proportion3has3at3least3four3nonconforming3units?
ANS:
a.
Number3Nonconforming Frequency Relative3Frequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
The3relative3 frequencies3don’t3add3up3exactly3to31because3they3have3been3rounded
b.3The3number3of3batches3with3at3most343nonconforming3items3is37+12+13+14+6=52,3which3is3a3proportion3of35
2/60=.867.3The3proportion3of3batches3with3(strictly)3fewer3than343nonconforming3items3is346/60=.767.
PTS:3 3 1
7. The3number3of3contaminating3particles3on3a3silicon3wafer3prior3to3a3certain3rinsing3process3was3determined3for3
each3wafer3in3a3sample3size3100,3resulting3in3the3following3frequencies:
Number3of3 particles Frequency Number3of3 particles Frequency
0 1 8 12
1 2 9 4
2 3 10 5
3 12 11 3
4 11 12 1
5 15 13 2
6 18 14 1
7 10
a. What3proportion3of3the3sampled3wafers3had3at3least3two3particles?3At3least3six3particles?
b. What3proportion3of3the3sampled3wafers3had3between3four3and3nine3particles,3inclusive?3Strictly3between3four3
and3nine3particles?
ANS:
a. From3this3frequency3distribution,3the3proportion3of3wafers3that3contained3at3least3two3particles3is3(100-1-2)/1003=
.97,3or397%.3In3a3similar3fashion,3the3proportion3containing3at3least363particles3is3(1003–31-2-3-12-11-
15)/1003=356/1003=3.56,3or356%.
b. The3proportion3containing3between343and393particles3inclusive3is3(11+15+18+10+12+4)/1003=370/1003=3.70
,3or370%.3The3proportion3that3contain3strictly3between343and393(meaning3strictly3more3than343and3strictly3les
s3than39)3is3(15+318+10+12)/100=355/1003=3.55,3or355%.
3 3 3 3 3 3 3 3
d The Sciences 8th Ed by Jay L. Devore.
3 3 3 3 3 3 3 3
Chapter313–3Overview3and3Descriptive3Statistics
SHORT3ANSWER
1. Give3one3possible3sample3of3size343from3each3of3the3following3populations:
a. All3daily3newspapers3published3in3the3United3States
b. All3companies3listed3on3the3New3York3Stock3Exchange
c. All3students3at3your3college3or3university
d. All3grade3point3averages3of3students3at3your3college3or3university
ANS:
a. Houston3Chronicle,3Des3Moines3Register,3Chicago3Tribune,3Washington3Post
b. Capital3One,3Campbell3Soup,3Merrill3Lynch,3Pulitzer
c. John3Anderson,3Emily3Black,3Bill3 Carter,3Kay3Davis
d. 2.58.32.96,33.51,33.69
PTS:3 3 1
2. A3Southern3State3University3system3consists3of3233campuses.3An3administrator3wishes3to3make3an3inference3ab
out3the3average3distance3between3the3hometowns3of3students3and3their3campuses.3Describe3and3discuss3several3d
ifferent3sampling3methods3that3might3be3employed.3Would3this3be3an3enumerative3or3an3analytic3study?3Explai
n3your3reasoning.
ANS:
One3could3take3a3simple3random3sample3of3students3from3all3students3in3the3California3State3University3system3a
nd3ask3each3student3in3the3sample3to3report3the3distance3from3their3hometown3to3campus.3Alternatively,3the3sam
ple3could3be3generated3by3taking3a3stratified3random3sample3by3taking3a3simple3random3sample3from3each3of3th
e3233campuses3and3again3asking3each3student3in3the3sample3to3report3the3distance3from3their3hometown3to3camp
us.
Certain3problems3might3arise3with3self3reporting3of3distances,3such3as3recording3error3or3poor3recall.3This3study3is3enu
merative3because3there3exists3a3finite,3identifiable3population3of3objects3from3which3to3sample.
PTS:3 3 1
3. A3Michigan3city3divides3naturally3into3ten3district3neighborhoods.3How3might3a3real3estate3appraiser3select3a3sa
mple3of3single-
family3homes3that3could3be3used3as3a3basis3for3developing3an3equation3to3predict3appraised3value3from3characte
ristics3such3as3age,3size,3number3of3bathrooms,3and3distance3to3the3nearest3school,3and3so3on?3 Is3the3study3enu
merative3or3analytic?
ANS:
One3could3generate3a3simple3random3sample3of3all3single3family3homes3in3the3city3or3a3stratified3random3sample
3by3taking3a3simple3random 3sample3from 3each3of3the3103district 3neighborhoods.3From 3each3of3the3homes3in3the3
sample3the3necessary3variables3would3be3collected.3This3would3be3an3enumerative3study3because3there3exists3a3f
inite,3identifiable3population3of3objects3from3which3to3sample.
, PTS:3 3 1
4. An3experiment3was3carried3out3to3study3how3flow3rate3through3a3solenoid3valve3in3an3automobile’s3pollution-
control3system3depended3on3three3factors:3 armature3lengths,3spring3load,3and3bobbin3depth.3 Two3different3level
s3(low3and3high)3of3each3factor3were3chosen,3and3a3single3observation3on3flow3was3made3for3each3combination3
of3levels.
a. The3resulting3data3set3consisted3of3how3many3observations?
b. Is3this3an3enumerative3or3analytic3study?3Explain3your3reasoning.
ANS:
a. Number3observations3equal3233 233 2=8
b. This3could3be3called3an3analytic3study3because3the3data3would3be3collected3on3an3existing3proc
ess.3There3is3no3sampling3frame.
PTS:3 3 1
5. The3accompanying3data3specific3gravity3values3for3various3wood3types3used3in3construction3.
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct 3a3stem-and-leaf3display3using3repeated3stems3and3comment3on3any3interesting3features3of3the3display.
ANS:
One3method3of3denoting3the3pairs3of3stems3having3equal3values3is3to3denote3the3stem3by3L,3for3‘low’3and3the3se
cond3stem3by3H,3for3‘high’.3 Using3this3notation,3the3stem-and-leaf3display3would3appear3as3follows:
3L 1 stem:3tenths
3H 56678 leaf:3 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The3stem-and-
leaf3display3on3the3previous3page3shows3that3.453is3a3good3representative3value3for3the3data.3 In3addition,3the3dis
play3is3not3symmetric3and3appears3to3be3positively3skewed.3 The3spread3of3the3data3is3.753-
3.313=3.44,3which3is3.44/.453=3.9783or3about 398%3of3the3typical 3value3of3.45.3 This3constitutes 3a3reasonably3large
3amount 3of3variation3in3the3data.3 The3data3value3.753is3a3possible3outlier.
PTS:3 3 1
6. Temperature3transducers3of3a3certain3type3are3shipped3in3batches3of350.3 A3sample3of3603batches3was3selected,
3and3the3number 3of3transducers3in3each3batch3not 3conforming3to3design3specifications 3was3determined,3resulti
ng3in3the3following3data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
43 3 23 3 13 3
3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
13 3 23 3 43 3
0
5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
03 3 23 3 33 3
,2
, a. Determine3frequencies3and3relative3frequencies3for3the3observed3values3of3x3=3number3of
nonconforming3transducers3in3a3batch.
b. What3proportion3of3batches3in3the3sample3has3at3most3four3nonconforming3transducers?3What3proportion3
has3fewer3than3four?3What3proportion3has3at3least3four3nonconforming3units?
ANS:
a.
Number3Nonconforming Frequency Relative3Frequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
The3relative3 frequencies3don’t3add3up3exactly3to31because3they3have3been3rounded
b.3The3number3of3batches3with3at3most343nonconforming3items3is37+12+13+14+6=52,3which3is3a3proportion3of35
2/60=.867.3The3proportion3of3batches3with3(strictly)3fewer3than343nonconforming3items3is346/60=.767.
PTS:3 3 1
7. The3number3of3contaminating3particles3on3a3silicon3wafer3prior3to3a3certain3rinsing3process3was3determined3for3
each3wafer3in3a3sample3size3100,3resulting3in3the3following3frequencies:
Number3of3 particles Frequency Number3of3 particles Frequency
0 1 8 12
1 2 9 4
2 3 10 5
3 12 11 3
4 11 12 1
5 15 13 2
6 18 14 1
7 10
a. What3proportion3of3the3sampled3wafers3had3at3least3two3particles?3At3least3six3particles?
b. What3proportion3of3the3sampled3wafers3had3between3four3and3nine3particles,3inclusive?3Strictly3between3four3
and3nine3particles?
ANS:
a. From3this3frequency3distribution,3the3proportion3of3wafers3that3contained3at3least3two3particles3is3(100-1-2)/1003=
.97,3or397%.3In3a3similar3fashion,3the3proportion3containing3at3least363particles3is3(1003–31-2-3-12-11-
15)/1003=356/1003=3.56,3or356%.
b. The3proportion3containing3between343and393particles3inclusive3is3(11+15+18+10+12+4)/1003=370/1003=3.70
,3or370%.3The3proportion3that3contain3strictly3between343and393(meaning3strictly3more3than343and3strictly3les
s3than39)3is3(15+318+10+12)/100=355/1003=3.55,3or355%.
