STATS 201 CH 6 PROBABILITY
QUESTIONS QUESTIONS WITH
COMPLETE ANSWERS
1. aaA aasurvey aaof aathe aastudents aain aaa aapsychology aaclass aarevealed aathat aathere
aawere aa19 aafemales
and aa8 aamales. aaOt aathe aa19 aafemales, aaonly aa4 aahad aano aabrothers aaor aasisters,
aaand aa3 aaof aathe
males aawere aaalso aathe aaonly aachild aain aathe aahousehold. aaIf aaa aastudent aais
aarandomly aaselected
from aathis aaclass,
a. aaWhat aais aathe aaprobability aaof aaobtaining aaa aamale?
b. aaWhat aais aathe aaprobability aaof aaselecting aaa aastudent aawho aahas aaat aaleast aaone
aabrother aaor
sister?
c. aaWhat aais aathe aaprobability aaof aaselecting aaa aafemale aawho aahas aano aasiblings? aa-
aaAnswer aa1. aab. aa20/27
c. aa4/27
2. aaAj aaar aacontains aa10 aared aamarbles aaand aa30 aablue aamarbles.
a. aaIf aayou aarandomly aaselect aa1 aamarble aafrom aathe aajar, aawhat aais aathe aaprobability
aaof aaobtaining aaa aared aamarble?
b. aaIf aayou aatake aaa aarandom aasample aaof aan aa= aa3 aamarbles aafrom aathe aajar aaand
aathe aafirst aatwo
marbles aaare aaboth aablue, aawhat aais aathe aaprobability aathat aathe aathird aamarble aawill
aabe aared? aa- aaAnswer aa2. aaa. aap aa= aaf aa= aa0.25
b- aaP aa= aa45 aa= aa0.25. aaRemember aathat aarandom aasampling aarequires aasampling
aawith aareplacement.
3. aaSuppose aathat aayou aaare aagoing aato aaselect aaa aarandom aasample aaof aa/; aa= aa1
aascore aafrom aathe
distribution aain aaFigure aa6.2. aaFind aathe aafollowing aaprobabilities:
a. aap(X aa> aa2)
b. aap(X aa> aa5)
c. aap(X aa< aa3) aa- aaAnswer aa3. aaa. aap=7/10
b- aaP aa= aa0.1
, c- aaP aa= aam aa= aa0.3
1. aaFind aathe aaproportion aaof aaa aanormal aadistribution aathat aacorresponds aato aaeach
aaof aathe aafollowing aasections:
a. aaz aa< aa0.25
b. aaz aa> aa0.80
c. aaz aa< aa-1.50
d. aaz aa> aa-0.75 aa- aaAnswer aa1. aaa. aap aa~ aa0.5987
b. aap aa= aa0.2119
c. aap aa= aa0.0668
d. aap aa= aa0.7734
2. aaFor aaa aanormal aadistribution, aafind aathe aaz-score aalocation aathat aadivides aathe
aadistribution aaas
follows:
a. aaSeparate aathe aatop aa20% aafrom aathe aarest.
b. aaSeparate aathe aatop aa60% aafrom aathe aarest.
c. aaSeparate aathe aamiddle aa70% aafrom aathe aarest aa- aaAnswer aa2. aaa. aac aa= aa0.84
b. aaz aa= aa-0 aa.2 aa5
c. aaz aa= aa— aa1.04 aaand aa+ aa1.04
3. aaThe aatail aawill aabe aaon aathe aaright-hand aaside aaof aaa aanormal aadistribution aafor
aaany aapositive
z-score. aa(True aaor aafalse) aa- aaAnswer aaTrue
1. aaFor aaa aanormal aadistribution aawith aaa aamean aaof aa|a aa= aa60 aaand aaa aastandard
aadeviation aaof
ct aa= aa12, aafind aaeach aaprobability aavalue aarequested.
a. aap(X aa> aa66)
b. aap(X aa< aa75)
c. aap(X aa< aa57)
d. aap aa(48 aa< aaX aa< aa72) aa- aaAnswer aa1. aaa. aap aa= aa0.3085
b. aap aa= aa0.8944
c. aap aa= aa0.4013
d. aap aa= aa0.6826
2. aaScores aaon aathe aaMathematics aasection aaof aathe aaSAT aaReasoning aaTest aaform
aaa aanormal
distribution aawith aaa aamean aaof aa|i aa= aa500 aaand aaa aastandard aadeviation aaof aact aa=
aa100.
a. aaIf aathe aastate aacollege aaonly aaaccepts aastudents aawho aascore aain aathe aatop
aa60% aaon aathis aatest,
what aais aathe aaminimum aascore aaneeded aafor aaadmission?
b. aaWhat aais aathe aaminimum aascore aanecessary aato aabe aain aathe aatop aa10% aaof
aathe aadistribution?
QUESTIONS QUESTIONS WITH
COMPLETE ANSWERS
1. aaA aasurvey aaof aathe aastudents aain aaa aapsychology aaclass aarevealed aathat aathere
aawere aa19 aafemales
and aa8 aamales. aaOt aathe aa19 aafemales, aaonly aa4 aahad aano aabrothers aaor aasisters,
aaand aa3 aaof aathe
males aawere aaalso aathe aaonly aachild aain aathe aahousehold. aaIf aaa aastudent aais
aarandomly aaselected
from aathis aaclass,
a. aaWhat aais aathe aaprobability aaof aaobtaining aaa aamale?
b. aaWhat aais aathe aaprobability aaof aaselecting aaa aastudent aawho aahas aaat aaleast aaone
aabrother aaor
sister?
c. aaWhat aais aathe aaprobability aaof aaselecting aaa aafemale aawho aahas aano aasiblings? aa-
aaAnswer aa1. aab. aa20/27
c. aa4/27
2. aaAj aaar aacontains aa10 aared aamarbles aaand aa30 aablue aamarbles.
a. aaIf aayou aarandomly aaselect aa1 aamarble aafrom aathe aajar, aawhat aais aathe aaprobability
aaof aaobtaining aaa aared aamarble?
b. aaIf aayou aatake aaa aarandom aasample aaof aan aa= aa3 aamarbles aafrom aathe aajar aaand
aathe aafirst aatwo
marbles aaare aaboth aablue, aawhat aais aathe aaprobability aathat aathe aathird aamarble aawill
aabe aared? aa- aaAnswer aa2. aaa. aap aa= aaf aa= aa0.25
b- aaP aa= aa45 aa= aa0.25. aaRemember aathat aarandom aasampling aarequires aasampling
aawith aareplacement.
3. aaSuppose aathat aayou aaare aagoing aato aaselect aaa aarandom aasample aaof aa/; aa= aa1
aascore aafrom aathe
distribution aain aaFigure aa6.2. aaFind aathe aafollowing aaprobabilities:
a. aap(X aa> aa2)
b. aap(X aa> aa5)
c. aap(X aa< aa3) aa- aaAnswer aa3. aaa. aap=7/10
b- aaP aa= aa0.1
, c- aaP aa= aam aa= aa0.3
1. aaFind aathe aaproportion aaof aaa aanormal aadistribution aathat aacorresponds aato aaeach
aaof aathe aafollowing aasections:
a. aaz aa< aa0.25
b. aaz aa> aa0.80
c. aaz aa< aa-1.50
d. aaz aa> aa-0.75 aa- aaAnswer aa1. aaa. aap aa~ aa0.5987
b. aap aa= aa0.2119
c. aap aa= aa0.0668
d. aap aa= aa0.7734
2. aaFor aaa aanormal aadistribution, aafind aathe aaz-score aalocation aathat aadivides aathe
aadistribution aaas
follows:
a. aaSeparate aathe aatop aa20% aafrom aathe aarest.
b. aaSeparate aathe aatop aa60% aafrom aathe aarest.
c. aaSeparate aathe aamiddle aa70% aafrom aathe aarest aa- aaAnswer aa2. aaa. aac aa= aa0.84
b. aaz aa= aa-0 aa.2 aa5
c. aaz aa= aa— aa1.04 aaand aa+ aa1.04
3. aaThe aatail aawill aabe aaon aathe aaright-hand aaside aaof aaa aanormal aadistribution aafor
aaany aapositive
z-score. aa(True aaor aafalse) aa- aaAnswer aaTrue
1. aaFor aaa aanormal aadistribution aawith aaa aamean aaof aa|a aa= aa60 aaand aaa aastandard
aadeviation aaof
ct aa= aa12, aafind aaeach aaprobability aavalue aarequested.
a. aap(X aa> aa66)
b. aap(X aa< aa75)
c. aap(X aa< aa57)
d. aap aa(48 aa< aaX aa< aa72) aa- aaAnswer aa1. aaa. aap aa= aa0.3085
b. aap aa= aa0.8944
c. aap aa= aa0.4013
d. aap aa= aa0.6826
2. aaScores aaon aathe aaMathematics aasection aaof aathe aaSAT aaReasoning aaTest aaform
aaa aanormal
distribution aawith aaa aamean aaof aa|i aa= aa500 aaand aaa aastandard aadeviation aaof aact aa=
aa100.
a. aaIf aathe aastate aacollege aaonly aaaccepts aastudents aawho aascore aain aathe aatop
aa60% aaon aathis aatest,
what aais aathe aaminimum aascore aaneeded aafor aaadmission?
b. aaWhat aais aathe aaminimum aascore aanecessary aato aabe aain aathe aatop aa10% aaof
aathe aadistribution?
