Test Bank For Probability And Statistics For Engineering A
j8 j8 j8 j8 j8 j8 j8 j8
nd The Sciences 8th Ed by Jay L. Devore.
j8 j8 j8 j8 j8 j8 j8 j8
Chapterj81j8–j8Overviewj8andj8Descriptivej8Statistics
SHORTj8ANSWER
1. Givej8onej8possiblej8samplej8ofj8sizej84j8fromj8eachj8ofj8thej8followingj8populations:
a. Allj8dailyj8newspapersj8publishedj8inj8thej8Unitedj8States
b. Allj8companiesj8listedj8onj8thej8Newj8Yorkj8Stockj8Exchange
c. Allj8studentsj8atj8yourj8collegej8orj8university
d. Allj8gradej8pointj8averagesj8ofj8studentsj8atj8yourj8collegej8orj8university
ANS:
a. Houstonj8Chronicle,j8Desj8Moinesj8Register,j8Chicagoj8Tribune,j8Washingtonj8Post
b. Capitalj8One,j8Campbellj8Soup,j8Merrillj8Lynch,j8Pulitzer
c. Johnj8Anderson,j8Emilyj8Black,j8Billj 8 Carter,j8Kayj8Davis
d. 2.58.j82.96,j83.51,j83.69
PTS:j 8 j 8 1
2. Aj8Southernj8Statej8Universityj8systemj8consistsj8ofj823j8campuses.j8Anj8administratorj8wishesj8toj8makej8anj8infere
ncej8aboutj8thej8averagej8distancej8betweenj8thej8hometownsj8ofj8studentsj8andj8theirj8campuses.j8Describej8andj8dis
cussj8severalj8differentj8samplingj8methodsj8thatj8mightj8bej8employed.j8Wouldj8thisj8bej8anj8enumerativej8orj8anj8a
nalyticj8study?j8Explainj8yourj8reasoning.
ANS:
Onej8couldj8takej8aj8simplej8randomj8samplej8ofj8studentsj8fromj8allj8studentsj8inj8thej8Californiaj8Statej8Universityj8s
ystemj8andj8askj8eachj8studentj8inj8thej8samplej8toj8reportj8thej8distancej8fromj8theirj8hometownj8toj8campus.j8Altern
atively,j8thej8samplej8couldj8bej8generatedj8byj8takingj8aj8stratifiedj8randomj8samplej8byj8takingj8aj8simplej8randomj8
samplej8fromj8eachj8ofj8thej823j8campusesj8andj8againj8askingj8eachj8studentj8inj8thej8samplej8toj8reportj8thej8distanc
ej8fromj8theirj8hometownj8toj8campus.
Certainj8problemsj8mightj8arisej8withj8selfj8reportingj8ofj8distances,j8suchj8asj8recordingj8errorj8orj8poorj8recall.j8Thisj8stud
yj8isj8enumerativej8becausej8therej8existsj8aj8finite,j8identifiablej8populationj8ofj8objectsj8fromj8whichj8toj8sample.
PTS:j 8 j 8 1
3. Aj8Michiganj8cityj8dividesj8naturallyj8intoj8tenj8districtj8neighborhoods.j8Howj8mightj8aj8realj8estatej8appraiserj8selec
tj8aj8samplej8ofj8single-
familyj8homesj8thatj8couldj8bej8usedj8asj8aj8basisj8forj8developingj8anj8equationj8toj8predictj8appraisedj8valuej8fromj
8characteristicsj8suchj8asj8age,j8size,j8numberj8ofj8bathrooms,j8andj8distancej8toj8thej8nearestj8school,j8andj8soj8on?j
8 Isj8thej8studyj8enumerativej8orj8analytic?
ANS:
Onej8couldj8generatej8aj8simplej8randomj8samplej8ofj8allj8singlej8familyj8homesj8inj8thej8cityj8orj8aj8stratifiedj8random
j8samplej8byj8takingj8aj8simplej8randomj8samplej8fromj8eachj8ofj8thej810j8districtj8neighborhoods.j8Fromj8eachj8ofj8th
ej8homesj8inj8thej8samplej8thej8necessaryj8variablesj8wouldj8bej8collected.j8Thisj8wouldj8bej8anj8enumerativej8studyj8
becausej8therej8existsj8aj8finite,j8identifiablej8populationj8ofj8objectsj8fromj8whichj8toj8sample.
, PTS:j 8 j 8 1
4. Anj8experimentj8wasj8carriedj8outj8toj8studyj8howj8flowj8ratej8throughj8aj8solenoidj8valvej8inj8anj8automobile‘sj8pollu
tion-
controlj8systemj8dependedj8onj8threej8factors:j 8 armaturej8lengths,j8springj8load,j8andj8bobbinj8depth.j 8 Twoj8differe
ntj8levelsj8(lowj8andj8high)j8ofj8eachj8factorj8werej8chosen,j8andj8aj8singlej8observationj8onj8flowj8wasj8madej8forj8ea
chj8combinationj8ofj8levels.
a. Thej8resultingj8dataj8setj8consistedj8ofj8howj8manyj8observations?
b. Isj8thisj8anj8enumerativej8orj8analyticj8study?j8Explainj8yourj8reasoning.
ANS:
a. Numberj8observationsj8equalj82j8j8 2j8j 8 2=8
b. Thisj8couldj8bej8calledj8anj8analyticj8studyj8becausej8thej8dataj8wouldj8bej8collectedj8onj8anj8existin
gj8process.j8Therej8isj8noj8samplingj8frame.
PTS:j 8 j 8 1
5. Thej8accompanyingj8dataj8specificj8gravityj8valuesj8forj8variousj8woodj8typesj8usedj8inj8constructionj8.
.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
Constructj8aj8stem-and-leafj8displayj8usingj8repeatedj8stemsj8andj8commentj8onj8anyj8interestingj8featuresj8ofj8thej8display.
ANS:
Onej8methodj8ofj8denotingj8thej8pairsj8ofj8stemsj8havingj8equalj8valuesj8isj8toj8denotej8thej8stemj8byj8L,j8forj8‗low‘j8a
ndj8thej8secondj8stemj8byj8H,j8forj8‗high‘.j 8 Usingj8thisj8notation,j8thej8stem-and-
leafj8displayj8wouldj8appearj8asj8follows:
3L 1 stem:j8tenths
3H 56678 leaf:j 8 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
Thej8stem-and-
leafj8displayj8onj8thej8previousj8pagej8showsj8thatj8.45j8isj8aj8goodj8representativej8valuej8forj8thej8data.j 8 Inj8additio
n,j8thej8displayj8isj8notj8symmetricj8andj8appearsj8toj8bej8positivelyj8skewed.j 8 Thej8spreadj8ofj8thej8dataj8isj8.75j8-
j8.31j8=j8.44,j8whichj8isj8.44/.45j8=j8.978j8orj8aboutj898%j8ofj8thej8typicalj8valuej8ofj8.45.j 8 Thisj8constitutesj8aj8reaso
nablyj8largej8amountj8ofj8variationj8inj8thej8data.j 8 Thej8dataj8valuej8.75j8isj8aj8possiblej8outlier.
PTS:j 8 j 8 1
6. Temperaturej8transducersj8ofj8aj8certainj8typej8arej8shippedj8inj8batchesj8ofj850.j 8 Aj8samplej8ofj860j8batchesj8wasj8
selected,j8andj8thej8numberj8ofj8transducersj8inj8eachj8batchj8notj8conformingj8toj8designj8specificationsj8wasj8det
ermined,j8resultingj8inj8thej8followingj8data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
4j 8 j 8 2j 8 j 8
1j 8 j 8 3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
1j 8 j 8 2j 8 j 8
4j 8 j 8 0
,5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
0j 8 j 8 2j 8 j 8
3j 8 j 8 2
, a. Determinej8frequenciesj8andj8relativej8frequenciesj8forj8thej8observedj8valuesj8ofj8xj8=j8numberj8of
nonconformingj8transducersj8inj8aj8batch.
b. Whatj8proportionj8ofj8batchesj8inj8thej8samplej8hasj8atj8mostj8fourj8nonconformingj8transducers?j8Whatj8prop
ortionj8hasj8fewerj8thanj8four?j8Whatj8proportionj8hasj8atj8leastj8fourj8nonconformingj8units?
ANS:
a.
Numberj8Nonconforming Frequency Relativej8Frequency
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
Thej8relativej 8 frequenciesj8don’tj8addj8upj8exactlyj8toj81becausej8theyj8havej8beenj8rounded
b.j8Thej8numberj8ofj8batchesj8withj8atj8mostj84j8nonconformingj8itemsj8isj87+12+13+14+6=52,j8whichj8isj8aj8proporti
onj8ofj852/60=.867.j8Thej8proportionj8ofj8batchesj8withj8(strictly)j8fewerj8thanj84j8nonconformingj8itemsj8isj846/60
=.767.
PTS:j 8 j 8 1
7. Thej8numberj8ofj8contaminatingj8particlesj8onj8aj8siliconj8waferj8priorj8toj8aj8certainj8rinsingj8processj8wasj8determin
edj8forj8eachj8waferj8inj8aj8samplej8sizej8100,j8resultingj8inj8thej8followingj8frequencies:
Numberj8ofj 8 particles Frequency Numberj8ofj 8 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. Whatj8proportionj8ofj8thej8sampledj8wafersj8hadj8atj8leastj8twoj8particles?j8Atj8leastj8sixj8particles?
b. Whatj8proportionj8ofj8thej8sampledj8wafersj8hadj8betweenj8fourj8andj8ninej8particles,j8inclusive?j8Strictlyj8betwee
nj8fourj8andj8ninej8particles?
ANS:
a. Fromj8thisj8frequencyj8distribution,j8thej8proportionj8ofj8wafersj8thatj8containedj8atj8leastj8twoj8particlesj8isj8(100-1-
2)/100j8=
.97,j8orj897%.j8Inj8aj8similarj8fashion,j8thej8proportionj8containingj8atj8leastj86j8particlesj8isj8(100j8–j81-2-3-12-
11-15)/100j8=j856/100j8=j8.56,j8orj856%.
b. Thej8proportionj8containingj8betweenj84j8andj89j8particlesj8inclusivej8isj8(11+15+18+10+12+4)/100j8=j870/100j
8=j8.70,j8orj870%.j8Thej8proportionj8thatj8containj8strictlyj8betweenj84j8andj89j8(meaningj8strictlyj8morej8thanj84j8
andj8strictlyj8lessj8thanj89)j8isj8(15+j818+10+12)/100=j855/100j8=j8.55,j8orj855%.
j8 j8 j8 j8 j8 j8 j8 j8
nd The Sciences 8th Ed by Jay L. Devore.
j8 j8 j8 j8 j8 j8 j8 j8
Chapterj81j8–j8Overviewj8andj8Descriptivej8Statistics
SHORTj8ANSWER
1. Givej8onej8possiblej8samplej8ofj8sizej84j8fromj8eachj8ofj8thej8followingj8populations:
a. Allj8dailyj8newspapersj8publishedj8inj8thej8Unitedj8States
b. Allj8companiesj8listedj8onj8thej8Newj8Yorkj8Stockj8Exchange
c. Allj8studentsj8atj8yourj8collegej8orj8university
d. Allj8gradej8pointj8averagesj8ofj8studentsj8atj8yourj8collegej8orj8university
ANS:
a. Houstonj8Chronicle,j8Desj8Moinesj8Register,j8Chicagoj8Tribune,j8Washingtonj8Post
b. Capitalj8One,j8Campbellj8Soup,j8Merrillj8Lynch,j8Pulitzer
c. Johnj8Anderson,j8Emilyj8Black,j8Billj 8 Carter,j8Kayj8Davis
d. 2.58.j82.96,j83.51,j83.69
PTS:j 8 j 8 1
2. Aj8Southernj8Statej8Universityj8systemj8consistsj8ofj823j8campuses.j8Anj8administratorj8wishesj8toj8makej8anj8infere
ncej8aboutj8thej8averagej8distancej8betweenj8thej8hometownsj8ofj8studentsj8andj8theirj8campuses.j8Describej8andj8dis
cussj8severalj8differentj8samplingj8methodsj8thatj8mightj8bej8employed.j8Wouldj8thisj8bej8anj8enumerativej8orj8anj8a
nalyticj8study?j8Explainj8yourj8reasoning.
ANS:
Onej8couldj8takej8aj8simplej8randomj8samplej8ofj8studentsj8fromj8allj8studentsj8inj8thej8Californiaj8Statej8Universityj8s
ystemj8andj8askj8eachj8studentj8inj8thej8samplej8toj8reportj8thej8distancej8fromj8theirj8hometownj8toj8campus.j8Altern
atively,j8thej8samplej8couldj8bej8generatedj8byj8takingj8aj8stratifiedj8randomj8samplej8byj8takingj8aj8simplej8randomj8
samplej8fromj8eachj8ofj8thej823j8campusesj8andj8againj8askingj8eachj8studentj8inj8thej8samplej8toj8reportj8thej8distanc
ej8fromj8theirj8hometownj8toj8campus.
Certainj8problemsj8mightj8arisej8withj8selfj8reportingj8ofj8distances,j8suchj8asj8recordingj8errorj8orj8poorj8recall.j8Thisj8stud
yj8isj8enumerativej8becausej8therej8existsj8aj8finite,j8identifiablej8populationj8ofj8objectsj8fromj8whichj8toj8sample.
PTS:j 8 j 8 1
3. Aj8Michiganj8cityj8dividesj8naturallyj8intoj8tenj8districtj8neighborhoods.j8Howj8mightj8aj8realj8estatej8appraiserj8selec
tj8aj8samplej8ofj8single-
familyj8homesj8thatj8couldj8bej8usedj8asj8aj8basisj8forj8developingj8anj8equationj8toj8predictj8appraisedj8valuej8fromj
8characteristicsj8suchj8asj8age,j8size,j8numberj8ofj8bathrooms,j8andj8distancej8toj8thej8nearestj8school,j8andj8soj8on?j
8 Isj8thej8studyj8enumerativej8orj8analytic?
ANS:
Onej8couldj8generatej8aj8simplej8randomj8samplej8ofj8allj8singlej8familyj8homesj8inj8thej8cityj8orj8aj8stratifiedj8random
j8samplej8byj8takingj8aj8simplej8randomj8samplej8fromj8eachj8ofj8thej810j8districtj8neighborhoods.j8Fromj8eachj8ofj8th
ej8homesj8inj8thej8samplej8thej8necessaryj8variablesj8wouldj8bej8collected.j8Thisj8wouldj8bej8anj8enumerativej8studyj8
becausej8therej8existsj8aj8finite,j8identifiablej8populationj8ofj8objectsj8fromj8whichj8toj8sample.
, PTS:j 8 j 8 1
4. Anj8experimentj8wasj8carriedj8outj8toj8studyj8howj8flowj8ratej8throughj8aj8solenoidj8valvej8inj8anj8automobile‘sj8pollu
tion-
controlj8systemj8dependedj8onj8threej8factors:j 8 armaturej8lengths,j8springj8load,j8andj8bobbinj8depth.j 8 Twoj8differe
ntj8levelsj8(lowj8andj8high)j8ofj8eachj8factorj8werej8chosen,j8andj8aj8singlej8observationj8onj8flowj8wasj8madej8forj8ea
chj8combinationj8ofj8levels.
a. Thej8resultingj8dataj8setj8consistedj8ofj8howj8manyj8observations?
b. Isj8thisj8anj8enumerativej8orj8analyticj8study?j8Explainj8yourj8reasoning.
ANS:
a. Numberj8observationsj8equalj82j8j8 2j8j 8 2=8
b. Thisj8couldj8bej8calledj8anj8analyticj8studyj8becausej8thej8dataj8wouldj8bej8collectedj8onj8anj8existin
gj8process.j8Therej8isj8noj8samplingj8frame.
PTS:j 8 j 8 1
5. Thej8accompanyingj8dataj8specificj8gravityj8valuesj8forj8variousj8woodj8typesj8usedj8inj8constructionj8.
.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
Constructj8aj8stem-and-leafj8displayj8usingj8repeatedj8stemsj8andj8commentj8onj8anyj8interestingj8featuresj8ofj8thej8display.
ANS:
Onej8methodj8ofj8denotingj8thej8pairsj8ofj8stemsj8havingj8equalj8valuesj8isj8toj8denotej8thej8stemj8byj8L,j8forj8‗low‘j8a
ndj8thej8secondj8stemj8byj8H,j8forj8‗high‘.j 8 Usingj8thisj8notation,j8thej8stem-and-
leafj8displayj8wouldj8appearj8asj8follows:
3L 1 stem:j8tenths
3H 56678 leaf:j 8 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
Thej8stem-and-
leafj8displayj8onj8thej8previousj8pagej8showsj8thatj8.45j8isj8aj8goodj8representativej8valuej8forj8thej8data.j 8 Inj8additio
n,j8thej8displayj8isj8notj8symmetricj8andj8appearsj8toj8bej8positivelyj8skewed.j 8 Thej8spreadj8ofj8thej8dataj8isj8.75j8-
j8.31j8=j8.44,j8whichj8isj8.44/.45j8=j8.978j8orj8aboutj898%j8ofj8thej8typicalj8valuej8ofj8.45.j 8 Thisj8constitutesj8aj8reaso
nablyj8largej8amountj8ofj8variationj8inj8thej8data.j 8 Thej8dataj8valuej8.75j8isj8aj8possiblej8outlier.
PTS:j 8 j 8 1
6. Temperaturej8transducersj8ofj8aj8certainj8typej8arej8shippedj8inj8batchesj8ofj850.j 8 Aj8samplej8ofj860j8batchesj8wasj8
selected,j8andj8thej8numberj8ofj8transducersj8inj8eachj8batchj8notj8conformingj8toj8designj8specificationsj8wasj8det
ermined,j8resultingj8inj8thej8followingj8data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
4j 8 j 8 2j 8 j 8
1j 8 j 8 3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
1j 8 j 8 2j 8 j 8
4j 8 j 8 0
,5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
0j 8 j 8 2j 8 j 8
3j 8 j 8 2
, a. Determinej8frequenciesj8andj8relativej8frequenciesj8forj8thej8observedj8valuesj8ofj8xj8=j8numberj8of
nonconformingj8transducersj8inj8aj8batch.
b. Whatj8proportionj8ofj8batchesj8inj8thej8samplej8hasj8atj8mostj8fourj8nonconformingj8transducers?j8Whatj8prop
ortionj8hasj8fewerj8thanj8four?j8Whatj8proportionj8hasj8atj8leastj8fourj8nonconformingj8units?
ANS:
a.
Numberj8Nonconforming Frequency Relativej8Frequency
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
Thej8relativej 8 frequenciesj8don’tj8addj8upj8exactlyj8toj81becausej8theyj8havej8beenj8rounded
b.j8Thej8numberj8ofj8batchesj8withj8atj8mostj84j8nonconformingj8itemsj8isj87+12+13+14+6=52,j8whichj8isj8aj8proporti
onj8ofj852/60=.867.j8Thej8proportionj8ofj8batchesj8withj8(strictly)j8fewerj8thanj84j8nonconformingj8itemsj8isj846/60
=.767.
PTS:j 8 j 8 1
7. Thej8numberj8ofj8contaminatingj8particlesj8onj8aj8siliconj8waferj8priorj8toj8aj8certainj8rinsingj8processj8wasj8determin
edj8forj8eachj8waferj8inj8aj8samplej8sizej8100,j8resultingj8inj8thej8followingj8frequencies:
Numberj8ofj 8 particles Frequency Numberj8ofj 8 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. Whatj8proportionj8ofj8thej8sampledj8wafersj8hadj8atj8leastj8twoj8particles?j8Atj8leastj8sixj8particles?
b. Whatj8proportionj8ofj8thej8sampledj8wafersj8hadj8betweenj8fourj8andj8ninej8particles,j8inclusive?j8Strictlyj8betwee
nj8fourj8andj8ninej8particles?
ANS:
a. Fromj8thisj8frequencyj8distribution,j8thej8proportionj8ofj8wafersj8thatj8containedj8atj8leastj8twoj8particlesj8isj8(100-1-
2)/100j8=
.97,j8orj897%.j8Inj8aj8similarj8fashion,j8thej8proportionj8containingj8atj8leastj86j8particlesj8isj8(100j8–j81-2-3-12-
11-15)/100j8=j856/100j8=j8.56,j8orj856%.
b. Thej8proportionj8containingj8betweenj84j8andj89j8particlesj8inclusivej8isj8(11+15+18+10+12+4)/100j8=j870/100j
8=j8.70,j8orj870%.j8Thej8proportionj8thatj8containj8strictlyj8betweenj84j8andj89j8(meaningj8strictlyj8morej8thanj84j8
andj8strictlyj8lessj8thanj89)j8isj8(15+j818+10+12)/100=j855/100j8=j8.55,j8orj855%.
