Test Bank For Probability And Statistics For Engineering
79 79 79 79 79 79 79 79
And The Sciences 8th Ed by Jay L. Devore.
79 79 79 79 79 79 79 79
Chapter79179–79Overview79and79Descriptive79Statistics
SHORT79ANSWER
1. Give79one79possible79sample79of79size79479from79each79of79the79following79populations:
a. All79daily79newspapers79published79in79the79United79States
b. All79companies79listed79on79the79New79York79Stock79Exchange
c. All79students79at79your79college79or79university
d. All79grade79point79averages79of79students79at79your79college79or79university
ANS:
a. Houston79Chronicle,79Des79Moines79Register,79Chicago79Tribune,79Washington79Post
b. Capital79One,79Campbell79Soup,79Merrill79Lynch,79Pulitzer
c. John79Anderson,79Emily79Black,79Bill7 9 Carter,79Kay79Davis
d. 2.58.792.96,793.51,793.69
PTS:7 9 7 9 1
2. A79Southern79State79University79system79consists79of792379campuses.79An79administrator79wishes79to79make79an79
inference79about79the79average79distance79between79the79hometowns79of79students79and79their79campuses.79Describ
e79and79discuss79several79different79sampling79methods79that79might79be79employed.79Would79this79be79an79enume
rative79or79an79analytic79study?79Explain79your79reasoning.
ANS:
One79could79take79a79simple79random79sample79of79students79from79all79students79in79the79California79State79Univer
sity79system79and79ask79each79student79in79the79sample79to79report79the79distance79from79their79hometown79to79cam
pus.79Alternatively,79the79sample79could79be79generated79by79taking79a79stratified79random79sample79by79taking79a7
9simple79random79sample79from79each79of79the792379campuses79and79again79asking79each79student79in79the79sampl
e79to79report79the79distance79from79their79hometown79to79campus.
Certain79problems79might79arise79with79self79reporting79of79distances,79such79as79recording79error79or79poor79recall.79This
79study79is79enumerative79because79there79exists79a79finite,79identifiable79population79of79objects79from79which79to79sam
ple.
PTS:7 9 7 9 1
3. A79Michigan79city79divides79naturally79into79ten79district79neighborhoods.79How79might79a79real79estate79appraiser7
9select79a79sample79of79single-
family79homes79that79could79be79used79as79a79basis79for79developing79an79equation79to79predict79appraised79value7
9from79characteristics79such79as79age,79size,79number79of79bathrooms,79and79distance79to79the79nearest79school,79a
nd79so79on?7 9 Is79the79study79enumerative79or79analytic?
ANS:
One79could79generate79a79simple79random79sample79of79all79single79family79homes79in79the79city79or79a79stratified79r
andom79sample79by79taking79a79simple79random79sample79from79each79of79the791079district79neighborhoods.79From
79each79of79the79homes79in79the79sample79the79necessary79variables79would79be79collected.79This79would79be79an79
enumerative79study79because79there79exists79a79finite,79identifiable79population79of79objects79from79which79to79sam
ple.
, PTS:7 9 7 9 1
4. An79experiment79was79carried79out79to79study79how79flow79rate79through79a79solenoid79valve79in79an79automobile‘s
79pollution-
control79system79depended79on79three79factors:7 9 armature79lengths,79spring79load,79and79bobbin79depth.7 9 Two79d
ifferent79levels79(low79and79high)79of79each79factor79were79chosen,79and79a79single79observation79on79flow79was79
made79for79each79combination79of79levels.
a. The79resulting79data79set79consisted79of79how79many79observations?
b. Is79this79an79enumerative79or79analytic79study?79Explain79your79reasoning.
ANS:
a. Number79observations79equal7927979 2797 9 2=8
b. This79could79be79called79an79analytic79study79because79the79data79would79be79collected79on79an79e
xisting79process.79There79is79no79sampling79frame.
PTS:7 9 7 9 1
5. The79accompanying79data79specific79gravity79values79for79various79wood79types79used79in79construction79.
.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
Construct79a79stem-and-
leaf79display79using79repeated79stems79and79comment79on79any79interesting79features79of79the79display.
ANS:
One79method79of79denoting79the79pairs79of79stems79having79equal79values79is79to79denote79the79stem79by79L,79for79‗l
ow‘79and79the79second79stem79by79H,79for79‗high‘.7 9 Using79this79notation,79the79stem-and-
leaf79display79would79appear79as79follows:
3L 1 stem:79tenth
s
3H 56678 leaf:7 9 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The79stem-and-
leaf79display79on79the79previous79page79shows79that79.4579is79a79good79representative79value79for79the79data.7 9 In79
addition,79the79display79is79not79symmetric79and79appears79to79be79positively79skewed.7 9 The79spread79of79the79data
79is79.7579-
79.3179=79.44,79which79is79.44/.4579=79.97879or79about7998%79of79the79typical79value79of79.45.7 9 This79constitutes79
a79reasonably79large79amount79of79variation79in79the79data.7 9 The79data79value79.7579is79a79possible79outlier.
PTS:7 9 7 9 1
6. Temperature79transducers79of79a79certain79type79are79shipped79in79batches79of7950.7 9 A79sample79of796079batches
79was79selected,79and79the79number79of79transducers79in79each79batch79not79conforming79to79design79specificatio
ns79was79determined,79resulting79in79the79following79data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
47 9 7 9 27 9 7
9 17 9 7 9 3
,2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
17 9 7 9 27 9 7
9 47 9 7 9 0
5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
07 9 7 9 27 9 7
9 37 9 7 9 2
, a. Determine79frequencies79and79relative79frequencies79for79the79observed79values79of79x79=79number79of
nonconforming79transducers79in79a79batch.
b. What79proportion79of79batches79in79the79sample79has79at79most79four79nonconforming79transducers?79What79
proportion79has79fewer79than79four?79What79proportion79has79at79least79four79nonconforming79units?
ANS:
a.
Number79Nonconforming Frequency Relative79Frequency
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
The79relative7 9 frequencies79don’t79add79up79exactly79to791because79they79have79been79rounded
b.79The79number79of79batches79with79at79most79479nonconforming79items79is797+12+13+14+6=52,79which79is79a79pr
oportion79of7952/60=.867.79The79proportion79of79batches79with79(strictly)79fewer79than79479nonconforming79item
s79is7946/60=.767.
PTS:7 9 7 9 1
7. The79number79of79contaminating79particles79on79a79silicon79wafer79prior79to79a79certain79rinsing79process79was79de
termined79for79each79wafer79in79a79sample79size79100,79resulting79in79the79following79frequencies:
Number79of7 9 particles Frequency Number79of7 9 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. What79proportion79of79the79sampled79wafers79had79at79least79two79particles?79At79least79six79particles?
b. What79proportion79of79the79sampled79wafers79had79between79four79and79nine79particles,79inclusive?79Strictly79be
tween79four79and79nine79particles?
ANS:
a. From79this79frequency79distribution,79the79proportion79of79wafers79that79contained79at79least79two79particles79is79(100-
1-2)/10079=
.97,79or7997%.79In79a79similar79fashion,79the79proportion79containing79at79least79679particles79is79(10079–791-2-
3-12-11-15)/10079=7956/10079=79.56,79or7956%.
b. The79proportion79containing79between79479and79979particles79inclusive79is79(11+15+18+10+12+4)/10079=7970/
10079=79.70,79or7970%.79The79proportion79that79contain79strictly79between79479and79979(meaning79strictly79mor
e79than79479and79strictly79less79than799)79is79(15+7918+10+12)/100=7955/10079=79.55,79or7955%.
79 79 79 79 79 79 79 79
And The Sciences 8th Ed by Jay L. Devore.
79 79 79 79 79 79 79 79
Chapter79179–79Overview79and79Descriptive79Statistics
SHORT79ANSWER
1. Give79one79possible79sample79of79size79479from79each79of79the79following79populations:
a. All79daily79newspapers79published79in79the79United79States
b. All79companies79listed79on79the79New79York79Stock79Exchange
c. All79students79at79your79college79or79university
d. All79grade79point79averages79of79students79at79your79college79or79university
ANS:
a. Houston79Chronicle,79Des79Moines79Register,79Chicago79Tribune,79Washington79Post
b. Capital79One,79Campbell79Soup,79Merrill79Lynch,79Pulitzer
c. John79Anderson,79Emily79Black,79Bill7 9 Carter,79Kay79Davis
d. 2.58.792.96,793.51,793.69
PTS:7 9 7 9 1
2. A79Southern79State79University79system79consists79of792379campuses.79An79administrator79wishes79to79make79an79
inference79about79the79average79distance79between79the79hometowns79of79students79and79their79campuses.79Describ
e79and79discuss79several79different79sampling79methods79that79might79be79employed.79Would79this79be79an79enume
rative79or79an79analytic79study?79Explain79your79reasoning.
ANS:
One79could79take79a79simple79random79sample79of79students79from79all79students79in79the79California79State79Univer
sity79system79and79ask79each79student79in79the79sample79to79report79the79distance79from79their79hometown79to79cam
pus.79Alternatively,79the79sample79could79be79generated79by79taking79a79stratified79random79sample79by79taking79a7
9simple79random79sample79from79each79of79the792379campuses79and79again79asking79each79student79in79the79sampl
e79to79report79the79distance79from79their79hometown79to79campus.
Certain79problems79might79arise79with79self79reporting79of79distances,79such79as79recording79error79or79poor79recall.79This
79study79is79enumerative79because79there79exists79a79finite,79identifiable79population79of79objects79from79which79to79sam
ple.
PTS:7 9 7 9 1
3. A79Michigan79city79divides79naturally79into79ten79district79neighborhoods.79How79might79a79real79estate79appraiser7
9select79a79sample79of79single-
family79homes79that79could79be79used79as79a79basis79for79developing79an79equation79to79predict79appraised79value7
9from79characteristics79such79as79age,79size,79number79of79bathrooms,79and79distance79to79the79nearest79school,79a
nd79so79on?7 9 Is79the79study79enumerative79or79analytic?
ANS:
One79could79generate79a79simple79random79sample79of79all79single79family79homes79in79the79city79or79a79stratified79r
andom79sample79by79taking79a79simple79random79sample79from79each79of79the791079district79neighborhoods.79From
79each79of79the79homes79in79the79sample79the79necessary79variables79would79be79collected.79This79would79be79an79
enumerative79study79because79there79exists79a79finite,79identifiable79population79of79objects79from79which79to79sam
ple.
, PTS:7 9 7 9 1
4. An79experiment79was79carried79out79to79study79how79flow79rate79through79a79solenoid79valve79in79an79automobile‘s
79pollution-
control79system79depended79on79three79factors:7 9 armature79lengths,79spring79load,79and79bobbin79depth.7 9 Two79d
ifferent79levels79(low79and79high)79of79each79factor79were79chosen,79and79a79single79observation79on79flow79was79
made79for79each79combination79of79levels.
a. The79resulting79data79set79consisted79of79how79many79observations?
b. Is79this79an79enumerative79or79analytic79study?79Explain79your79reasoning.
ANS:
a. Number79observations79equal7927979 2797 9 2=8
b. This79could79be79called79an79analytic79study79because79the79data79would79be79collected79on79an79e
xisting79process.79There79is79no79sampling79frame.
PTS:7 9 7 9 1
5. The79accompanying79data79specific79gravity79values79for79various79wood79types79used79in79construction79.
.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
Construct79a79stem-and-
leaf79display79using79repeated79stems79and79comment79on79any79interesting79features79of79the79display.
ANS:
One79method79of79denoting79the79pairs79of79stems79having79equal79values79is79to79denote79the79stem79by79L,79for79‗l
ow‘79and79the79second79stem79by79H,79for79‗high‘.7 9 Using79this79notation,79the79stem-and-
leaf79display79would79appear79as79follows:
3L 1 stem:79tenth
s
3H 56678 leaf:7 9 hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The79stem-and-
leaf79display79on79the79previous79page79shows79that79.4579is79a79good79representative79value79for79the79data.7 9 In79
addition,79the79display79is79not79symmetric79and79appears79to79be79positively79skewed.7 9 The79spread79of79the79data
79is79.7579-
79.3179=79.44,79which79is79.44/.4579=79.97879or79about7998%79of79the79typical79value79of79.45.7 9 This79constitutes79
a79reasonably79large79amount79of79variation79in79the79data.7 9 The79data79value79.7579is79a79possible79outlier.
PTS:7 9 7 9 1
6. Temperature79transducers79of79a79certain79type79are79shipped79in79batches79of7950.7 9 A79sample79of796079batches
79was79selected,79and79the79number79of79transducers79in79each79batch79not79conforming79to79design79specificatio
ns79was79determined,79resulting79in79the79following79data:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
47 9 7 9 27 9 7
9 17 9 7 9 3
,2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
17 9 7 9 27 9 7
9 47 9 7 9 0
5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
07 9 7 9 27 9 7
9 37 9 7 9 2
, a. Determine79frequencies79and79relative79frequencies79for79the79observed79values79of79x79=79number79of
nonconforming79transducers79in79a79batch.
b. What79proportion79of79batches79in79the79sample79has79at79most79four79nonconforming79transducers?79What79
proportion79has79fewer79than79four?79What79proportion79has79at79least79four79nonconforming79units?
ANS:
a.
Number79Nonconforming Frequency Relative79Frequency
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
The79relative7 9 frequencies79don’t79add79up79exactly79to791because79they79have79been79rounded
b.79The79number79of79batches79with79at79most79479nonconforming79items79is797+12+13+14+6=52,79which79is79a79pr
oportion79of7952/60=.867.79The79proportion79of79batches79with79(strictly)79fewer79than79479nonconforming79item
s79is7946/60=.767.
PTS:7 9 7 9 1
7. The79number79of79contaminating79particles79on79a79silicon79wafer79prior79to79a79certain79rinsing79process79was79de
termined79for79each79wafer79in79a79sample79size79100,79resulting79in79the79following79frequencies:
Number79of7 9 particles Frequency Number79of7 9 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. What79proportion79of79the79sampled79wafers79had79at79least79two79particles?79At79least79six79particles?
b. What79proportion79of79the79sampled79wafers79had79between79four79and79nine79particles,79inclusive?79Strictly79be
tween79four79and79nine79particles?
ANS:
a. From79this79frequency79distribution,79the79proportion79of79wafers79that79contained79at79least79two79particles79is79(100-
1-2)/10079=
.97,79or7997%.79In79a79similar79fashion,79the79proportion79containing79at79least79679particles79is79(10079–791-2-
3-12-11-15)/10079=7956/10079=79.56,79or7956%.
b. The79proportion79containing79between79479and79979particles79inclusive79is79(11+15+18+10+12+4)/10079=7970/
10079=79.70,79or7970%.79The79proportion79that79contain79strictly79between79479and79979(meaning79strictly79mor
e79than79479and79strictly79less79than799)79is79(15+7918+10+12)/100=7955/10079=79.55,79or7955%.
