MAT 142 – Topics In Math Spring 2014: Final Exam

MAT 142 – Topics In Math
Spring2014:FinalExam
Instructor:RobertFoth
PimaCommunityCollege,CommunityCampus
Answerthequestionsinthespacesprovided.Ifyouneedadditionalspaceuse
thebackofthepageandmakesuretheproblemnumberisreferencedwiththe
work.Ifscratchpaperisusedmakesuretoattachthepaperalongwiththe
examwhenitisturnedin.Youmustshowallworktoreceivefullcreditonthe
problem.Youmayuseacalculator(maynotuseacellphone).Thereisathree
hourtimelimit.Besuretoreadeachquestioncarefullyandfollowthe
instructionsgiven.Itispossibletoscoreover100%ontheexam.Goodluck!
Iwillgradeeachquestionbasedon:
1. Completeness‐Showingallofyourworkandhowyouderivedthe
answer.
2. Correctness‐Gettingthecorrectanswerisimportant,butIwillgive
partialcreditifyoushowyourwork.
3. Neatness‐Ineedtobeabletoreadyouranswer.IfIcannotreadyour
answer/work,thenyouwillreceive0pointsfortheproblem.
Az‐scoretableisattachedonthelastpageoftheexam(yesyouwillneedit).
StudentsName:________________________________________________________
SCORE
___________________/150
1.
Twobanksofferaccountthatcompoundtheinterestslightlydifferentlyfromeachother.
Theinformationforeachbankisbelow.
BankA:
Compoundsinterestmonthlyatanannualrateof3.8%
BankB:
Compoundsinterestcontinuouslyatanannualrateof3.8%
Computethevalueofa$250depositintoeachaccountfor2years.Showyourwork.
(8points)
2.
(6points)
Samhasbeensavingupforretirementandrealizeshewillhave$500,000savedupwhen
heretires.Samwantstotakeequalmonthlywithdrawalsfromtheaccountforatotalof
35yearsafterheretires.Iftheretirementaccounthasanannualrateof5.5%andis
compoundedmonthly,thenhowmuchcanhewithdraweachmonth?
3.
The growth of the average cost of textbooks per course at a small liberal arts college was
modeled with the following formula: Pn  110  (1  .045) n . If this models starts for the year
2003 as n = 0, then evaluate P13 and interpret this result in terms of the application. Make sure
to include such things as the cost of the textbooks per course and the year.
(8points)
4.
Alargedepartmentstoreisofferinga20%discountonyourpurchase.Atthecheckout
youaregivenanadditionaldiscountof15%forusingthestorescreditcard.Thissecond
discountistakenafterthefirstdiscountisapplied.Answerthefollowing:
(6pointseach)
(i)
(ii)
5.
Whatisthetotaldiscountonapurchaseof$200?
Findthetotalpercentdiscountofftheoriginalpriceof$200.
Is it possible if A and B are events from a probability experiment that P  A or B   1.15 ? Why
or why not
(6points)
6.
Givingatesttoagroupofstudents,thegradesandgenderaresummarizedbelow.Answer
thequestionbelowbasedonthistable.
Male
Female
Total
A
8
10
18
B
18
4
22
C
13
12
25
Total
39
26
65
(6pointseach)
(i)
(ii)
(iii)
7.
(6points)
Findtheprobabilityofrandomlyselectingastudentandthatstudentismale.
FindtheprobabilityofrandomlyselectingastudentthatismaleorhasearnedaB.
FindtheprobabilityofrandomlyselectingastudentisfemalegiventhestudenthadaB.
Acomputeruserhasdownloaded10songsusinganonlinefile‐sharingprogramand
wantstocreateaCD‐RwithfoursongstouseinhisportableCDplayer.Iftheorderthat
thesongsareplacedontheCD‐Risimportanttothem,howmanydifferentCD‐Rscould
hemakefromthe10songsavailabletohim?
8.
Inaclassroomthereare8girlsand7boys.TheclassistoelectaPresident,Vice
President,andaTreasurer.Whatistheprobabilityifstudentswereelectedatrandom
thatallthreepositionswerefilledbyboys?
(6points)
9.
Agroupofmathematiciansaregettingtogetherforaconference.Themembersare
comingfromthreecities:Tacoma,Puyallup,andOlympia.Thepreferencevotesforwhere
toholdtheconferencearegivenbelow(noticethenumberontoptellsyouhowmany
peoplevotedforthatpreferenceorder):
Total#
35
25
9
st
1 choice
Puyallup
Tacoma
Olympia
2ndchoice
Tacoma
Olympia
Tacoma
3rdchoice
Olympia
Puyallup
Puyallup
(i)
WhoisthewinnerofthiselectionusingtheBordaCountMethod?
(ii)
Howmanyvotesareneededtohaveamajority?
(6points)
(4points)
(iii)
(4points)
Doesyouranswerfrom(i)showthattheBordaCountmethodsatisfiestheCondorcet
Criterion?Explainyouranswer.
10.
Supposethispreferenceschedulegivestheresultsofanelectionamong3candidates,A,B,
andC.WhowinsusingCopeland’sMethod(alsoknownasPairwiseComparisons)?
Numberofvoters
1stchoice
2ndchoice
3rdchoice
20
A
C
B
19
B
C
A
5
C
B
A
(6points)
11.
Youhavebeengiventheopportunitytoinvestintwodifferentcompanies:companyAand
companyB.Bothcompaniesarereputable,andeachisworkingonpotentiallyimportant
scientificprojects.IfyouinvestincompanyAthereisa30%chancethatyoulose$30,000,
a50%chancethatyoubreakeven,anda20%chancethatyoumake$70,000.Ifyou
investincompanyBthereisa20%chancethatyoulose$75,000,a70%chancethatyou
breakeven,anda10%chancethatyoumake$150,000.Basedontheexpectedvalueof
each,whichinvestmentshouldyoumake?
(8points)
12.
(6points)
Onanormaldistributionthemeanisknowntobe50withastandarddeviationof15.
Whatpercentofobservationsfromthedistributionarefrom50to80?
13.
Foreachstatementbelowwritethecorrespondinglettertomatchittotheappropriate
typeofbias.Eachanswercanonlybeusedonce.
(2ptseach)
____
____
____
____
____
____
14.
Asurveyatyourworkplaceaskshowmanytimesyou haveusednarcoticsinthepast12months.
Alocalnewsstationasksviewerstophoneintheirchoice
inadailypoll.
Apoliticianwantstoknowhowpeopleinthedistrictfeel
aboutanewlaw.Heaskstenpeopleatrandomfromthe
audienceathisnextspeech.
Ateacherasksstudentsinaclasshowoftentheyfart. Thegunlobbyreleasesastudythatgunownersarein
generalhappierthanthosewhodonotownguns.
A.
LoadedQuestion
B.
Non‐response
C.
SamplingBias
D.
VoluntaryResponse
E.
Self‐InterestStudy
F.
PerceivedLackof
Anonymity
Aneighborhoodsurveyasks“Doyouthinkpeopleshould
playthatloudandannoyingRockandRollmusicafter8pm?”
Aparticularmanufacturerofcerealtriedtodeterminetheeffectivenessoftheircerealto
increaseattentivenessintheschoolclassroomforstudents.Inthestudystudentswere
randomlyassignedtoreceiveeitherabowlofcerealforbreakfastortheyweretoldto
eachnobreakfastbeforecomingtoschool.
(4ptseach)
(i)
(ii)
Wouldyouclassifythisasanobservationalstudyoranexperiment?Justifyyouranswer.
Identifyamajorflawwiththestudy.Whatcouldbedonetoimprovethisstudy?
15.
(6points)
16.
(i)
(6points)
(ii)
Isthestudentcorrectornot‐explainyouranswer.
Johnsawthattherewerefivestudentswhoscoreda10onthequizandthreethatscored
a8.Headdsup8and10toget18anddividesbytwoandstatedthatthemedianis9.
Belowisthescoresfor10studentswhotooktherecentquiz.Answerthequestionsbelow
basedonthisdata.
20,11,14,14,18,19,9,17,15,15
Findthemeanforthedata.
Findthemedian.
(6points)
(iii)
Woulditbemoreappropriatetorepresentthedatawithabargraphorahistogram?
Explainyouranswer.
(4points)
17.
(6points)
Asodamanufacturerfillsbottleswithameanof20.2ozandastandarddeviationof
.15oz.Whatpercentageofthebottleswillbefilledwithfewerthan20oz?Usethe
StandardNormalTabletohelpyouanswerthisquestion.
Standard Normal Values (Needed for at least one question on the exam)
MAT 142 Formula Page (Final)
Length
1 foot (ft) = 12 inches (in)
(ft)
1 mile = 5,280 feet
1000 millimeters (mm) = 1 meter (m)
meter
1000 meters (m) = 1 kilometer (km)
Capacity
1 cup = 8 fluid ounces (fl oz)
1 quart = 2 pints = 4 cups
cups
1000 milliliters (ml) = 1 liter (L)
absolute change
Relative change: starting quantity
Area
100 centimeters (cm) = 1
2.54 centimeters (cm) = 1 inch
Weight and Mass
1 pound (lb) = 16 ounces (oz)
1000 milligrams (mg) = 1 gram (g)
1000 grams = 1kilogram (kg)
1 kilogram = 2.2 pounds (on earth)
1 ton = 2000 pounds
1 pint = 2 cups
1 gallon = 4 quarts = 16
log  Ar   r log  A 
Distance
Volume
Rectangular Box: L W  H
Perimeter Rectangle: 2 L  2W
Circumference Circle: 2 r
Rectangle : L  W
Circle :  r
1 yard (yd) = 3 feet
2
Linear Growth
Cylinder:  r 2 h
Exponential Growth
Recursive form: Pn  Pn 1  d
Recursive form: Pn  1  r   Pn 1
Explicit form: Pn  P0  dn
Explicit form: Pn  P0 1  r 
Simple Interest
Compound Interest Discretely
A  P0 1  rt 
 r
A  P0 1  
 k
z  score 
x

P  E   1  P( E )
P  A | B 
n
Pr 

Compound Interest
Continuously
A  P0e rN
Nk
Annuity Formula
  r Nk 
d  1    1
 k 



PN 
r
 
k
n
Payout Annuity (also Loan Formula)
  r  N k 
d 1  1   
  k 

P0  
r
 
k
data value - mean
standard deviation
P( E ) 
P(A and B) = P(A) • P(B)
P  A and B 
P  B
Number of outcomes corresponding to the event E
Total number of equally - likely outcomes
P(A or B) = P(A) + P(B) – P(A and B)
n! = n • (n – 1) • (n – 2) ••• 3 • 2 • 1
n!
 n   n  1   n  2   n  r  1
(n  r )!
n
Cr 
n!
(n  r )!r!