Final Fall 2006

Final Fall 2006 - FALL HIDE FINAL EXAM SflLU'I'IDNE MATH...

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Unformatted text preview: FALL HIDE FINAL EXAM SflLU'I'IDNE MATH 213. DEGEMEER 13. Eflllfi Thin is a ml111inn eel Eur 1.11.: MaLI‘I 21F; fina1cm11mnn exam held I'rrm'. E:EIEI Ln I1:E|E| pH on deenday. Number 13. 3:15. There were ten. Frat-Items, weighted aqua“)- [l'or a tnLal of 1-30 paints}. Thee: sen-Ju- Linne are ealhller meme full and complete than anything 'I'E emuld have exp-Edna rmn: any studenL. Problem 1 {EU pte]. 3D marbles tore sitter-5g on o tat-fir 6 red. '9 Blue. and 15- y-ree-n. All! of the red marbles, 3 of the hie-e marbles, and! 1H a] the. green marbles 111-. entire-no! in dawn-Hole. hatntL-te. :1. child. pinged unlh them while. eating a piece n_|" pie. The. renaming Tatar-Heat were. mil. :15" the. child's rem-.h and remained elm-1.11.. fie] Drew o. pmhehtfihy tree tiger-thirty the situation. Be 311.11: hr heelude the Jofiete of euertteJ probabilities, and conditional: probabilities. {b} If a. mud-omqu selected moi-hie '53 covered in chocolate. who: :23 the mammary the: e e: mt? [c] If no mndomty aeietted morhte fie red. what is the probottttty that lit to melee-ed 1+1 :h-oeetete? {d} A-re the even-ts “red” and "covered tn. ehotoI-ote" indepen- dent? Sotehon. [a] 'T'I'Ie math-Ira: arr. parLiL'imtd. in it“: way-It: acmrdtng 1n EDIE“. and attending in whether they'll: covered in chu-onlrfle nr are clean. There at:I arxmdingly. him Why: Jenn can draw [11: [Tail 1']: the fleet, the fleet level of the tree :ie. heeed on color, and the eetohd level heaed oh ehooolatefcleah; in the aeeond, the fleet leefl ef the tree :ie. based out th-o|:r_'.]atell’i:leehI and the eeoohd ie haeed oh eolor. The two we}: are about eqhaJl].I eeejr. flu: fleet tree Lteee the ooLoI-firet approach. 01' eol.1.1:eeI you were inatt'heted to Iedute fratt'toha ho Lowemt tetma, ao ioatead of “UL-'15". for example. as a conditional probability in the tree. you should hat-e written "2.8". We have left the fractions umedueed to make it more obvious where they came from. Also. the eaJeuJati-Izun not the r‘ probabilitiea at the tight edge wee not, ett'jethr eel-taking. halted E-oti but they‘re too useful for the test of the problem, and nine: they're trivial to calculate. yeru ebulqu probably all-aye write them down. Here's the tint tree: 61‘" mm: PfCho-er‘ltfl = % R if; $3., Clem: PICJeeer'R] = t} .q 1 3I' Choc PfCho-Ef‘fl] = — wee “3' . - . 1 {5,33 Clem: PICJeeer B. = E {T alt? f IShoe PfCho-Er‘fl'l = E 1 5', Elena: PICJeEhr'Gj = a [:1 [he fiflDfil‘lt‘] p-nta'i'hle Lee: deeeripLi-nn, we have. ln mum. the number at chu-cnlale-Lntlered marble: and LE: numb-er DJ 1:15am. marl-flu. 'lII'hI\.rh'.\|1:Iel].I thre are. 1‘} ehncnlatae-cnwrhd mater [5 red, 3 Huh, and. [El green], 1HP'iILE I I dean marble: :rnr]I E blue, and 5 green]. Thie tree has the advantage that all the prohebllltjee ere ahead}I 1']: lowest tern-J: 5-D LLITII‘LIN 3 Fromm“ =15 PIGI‘Chu-cl =4, Pm I'Cieanl o PIii-I'Clcaiii 5‘; PIC. .-~ Cleau'l = 3' {hi PIRI Citric] Pf-Shnc: PI'RlChn-c: = _ PIRr‘Chh-c: _ PIRI'Chth - PIE-I'Choci I PIi—H'Choc'l' which from the tree in part [a} is 1 F'ITE|I:‘:i-m:'| = # = i a; 1" Ifi- Ifli‘ll 133 I? H b {If cause: this is even easier if you use the seq:de tree. the entiditiohai probability tifl‘i‘ ia. aheady built into the tree. [It] You can do this with in: oomputatiou, just a little thinking. you've mid that a“ of the ted tuai'blefi were muered in ehhoo— hateI sh ifjrou aelect a red marble: well. .thete'a. a rflfi'fi. theme it'a covered in chocolate... {If EDU‘E‘EE, you can also do the computation: PIChht’r‘R: F'l'ChoI:"F'.'I FIR] F'I'L'I'I'irim‘R: | PiiiLeanl R:' which from the tree is I-‘fChoI: “ii I 3.; PrCho: RI: =1. I 1.35 I III CI: use the second. tits: {ni} The events "th” and "Ch-acetate" ail: indhpcudmt ifanlzi only it PIRr'CIhntfl = PI'RIF’ICI'IL'I-efl. But from the tree. PIHI Elfin-I" [IF-I. whiJn: FIChh-C'l =P|R"-3h1x: |FfBI“Ch-x| | HEPCthI _I I I I I '5 ID .1. _ I? _E_ Sh the qUeetioi: is whether I _ 1 Q h: 5 ' 5 .m’ which 15 Mireiy I'n'lm. unn-n'lently. R and C an: int-lg]dean if and nn'ly if P:E|C: = FIR]. We've already oomputed theee in put [a]I and no, they Weren't equal. ‘t'urhiie it's a Little extra work: it may be mthwhile to build a probability tahie Emu: hue at the tteee. This is. an fellow: [with the iuuginei pmhahilitiee, the sum of the raw: and onlLoum, filled in]: -l:lnl- I I -|- SOLUTION! The trsJleatia-n from a tree Jilte Figure 1 ta a table is inane- diate; yau'te entering the prahahllitim yea entered at the far right of the ties- {1f Tau were wise.) U Pmblenr 2 [2|] lets]. Dee she-t by a. standard. filing-an phase!" has a. ED'R': prefab-titty af cause-1.9 L1 hits-aims, a 3% prefiatlility afeausifly 1 his pains, and a SU'i-i. prudent-titty af ewe-same 1 hit ale-late. fa] Find the suspected t'fli‘llE‘ and standard defiant-flan. ef the n.er- ee-r ‘r’ af hits-amasth arse shat by a flange-fl. pheser. {13] The Ming-an, cruiser EEJaar's Liver has the new Hewitt-am phase-re. which cause 55% mare damage in. hit paints than standard phasers. {Far erampI-e. when a standard phases causes 1' hit paints damage. the Barelliam. phasef' causes 3'. 2-: 1.15 1.5 hit paints damage.) Fin the eapeeied eat-ale |.l and standard deviates-n a a-_|" the number af hit paints far an: shat by Slflaat's Liver. [L'] We. Star-ship EnLerpfisr. can. take. up tea 6C1 hit pnmL-t he Inna being deslmymal. Find the pmhahflfly that a Hts-Janna firing standard phalanx-I: am.” denth the Finis-psi.“ math "1-D independent shale. Is this number exact nr hymn-mate? Eqatetin 111. the. spam hail-nu the. answer hnzes. Sadat-ten. t'au'te given the EaUaI'irLg tab-1e far the standard Hllagan phases: IIEIII IllEl [a] The expected 'L'EJUE: at 2': is t} :x: ELI-1 I 1 2-: I13- I 1 3x: :15 = 1.3- The standard deviatian can he aarnputed as LIKJI — [L3, and 50:11:41! eat-13 e as I 11 :s as = 2.1., Lhue II: = Frill-l: — ll: = In} — 1.3-I =fl.E1:_ ne Sinai];- {F 121.:"31 ta three decimals (as reg-mired by the insteuetiane}- {11] The rsnduatu variable which maids. hit paints e: Baeefliutu phasers is. era-:11}.- 1-25 times the tandem: eariahls which taunts hit paints iarstandard phasers; thsrsfare its expected value and standard dfi'n‘lit'lfll'i ate 115tin1ss thase quantities far stande phasers: [J = 1.1; 3-: LS = 1.615.. a = 1.2-1 3-: REM = C1355, taunde be three decimals. [s] The prahahility can he emanated exactly: aJJ yau have lJZI dI:I is build the three-level treeI and than 131.1in sapies afi each h1anth. up ta 11-0 levels, and hue]: traslt at" hit-paints as area travel thradgh the tree. That last Jere] is add-nay: it has 3‘” = lllFI-F'IF-[i'i-ifi‘lflfiti‘llflflfll finds! UH, an mi!th lhaL ian'L paal:l:||:a1. TL can 1.1-: sham-n that the l:|:1'|:I-1:Ii'l.l'|:clli.L].I all Eeltmg exactly rL hil-pninLa :LI: lh: mefliclenl at it" in “3.2 | 1.13:: | flu'iunl'l‘c. h'urhile 311a can'l do this 113' hand in any Inasmal'flr. tin-II:I campu lr.r WINE. li1-:i= Mathematt'm can urin- i1. :ll1 nn lime {WEIIL UflE'MF-i nemnel an 1113' MaEH-mk Pm): and the sun; hi the caefideute hi 1"“, x“, .- ., in” la U.UE1EF?S. This aJni'l-‘H' is exact ta seven deeimsJ pieces, and is what yere. she-aid estdre th- as yum- sesame. Alena, it leads th- the falls-wing graph: the red talurahs have as their height the era-rt prahahll— it]: efgstting I lit-paints; |:ee’t'e et'erlaid that with the naraaal BULIJTIIEIHE cur-ire with mean 51 and etanciard deviation J1.‘:"_'t‘:'tir1 {nee helcmr fer the erqflanatihn at why]. Liut ehr'i-mrely metre of thie ie pceeihle Eur a etudecnt taking the erzaru. Ii'n'hat clicl we have in mind? The answer iiiI We wanted yeti te- eepi'y the Gen-treat Limit Thee-rem if H1 deucitee the I:L'it paints cf the :l:,||:'a|:.2.111;”;F I: the hit pneetc at the eecclncl .1:h1:1tI Lhrclugh it:ng and we set x=xl l x; I "' I Ran. then the Central Liruit Theorem eaye that lit in uppmenetely normally distributed. Since Luci den-cc; 5.1.. cre- v’Ea-ceafliele 11.543961. [mate that we had Ln flee the standard deviatinn cell the IL tn more than three digit accuracy in crrder in gel the standard. deviaticm all it: tn three-digit accuracy]I we can apprmrmate lei—El _ eat—52.1. .-"‘ Here-1 4-91954} = err .3 1151-1155;. Filteeei=P{ Apprercicuatieg Le'iti'EE-i by 1.511. we Elect that Fill a; E a; 1.151! = IIIJMFI, henLie Fri-1 2:- 1.151] = 12.5 — 021-111 = fltlfila. Flcurriieh to three cle:cirr:aleI we Iwere lee-hing fier fltlljl ae yeur anewecr. Cempared tn the actual exact value at fl.DEiEFFii, thie ien't very impreeaitre. [t can be ircprmred quite a hit ueing the c1911- efitu‘icy cclrr'ec'ciclra Since net all Bf yeu were taught the centi- nuity cerreclien, we clicin't require you to use it; it ce-neiete. cnf ceruputing 595 — 51 ri.t~'3'i'6:1 Since Pia 11* 1.5.2] ISL-[1513, thie ie a rcueh better appreicirua- ticm tn the true Halue. Fixafi'fljl mfg: J=P|ze 1.5115111. We didn't aelc I'm the prehebe'lity that Stratum-’3 Lite-er- ceulcl cleetrciy the Enterprise L1: a1-EI e.h1:1taI altbeugh ecu-rue etudetite calculated it. [The prehlere explicitly eeyeI “etanclarcl phase-re"- Still1 we gave meet at the credit fer euch an auew‘er.) But there ir. an interesting imam ir1 audit 1e nlnrtatirm. With standard. phase”, the expected damage rmn'l 3m chat: 1:: 4|: 2-: l.3 = F12 hit painte— teer: than the antnunt iL Lat-:er: th dutrcly the Enter-price. We're nut surprised that the prvrrhia'hilit].I cri' dettrvnying the Enterprwre ie dnly H.315”. With Hurelhum phairerlliI which are duly 15% 1'.r.c|re efficient, the gee-bability cf eieetre-yirrg the Enter-pm: turtle cut tn he ilklii'ii, tub-re than meme taneer as great- it might be well be remember thie eert cif calculaticm the heart time the Fentagcei eelce fer a fighter which ceruueutatcce renearlc ie “bully” 15% better than the current cluee. Eur-ruetituee that 55% can buy year a 1103993 irclr-rm'ercent in lrilling capacity. Finally. there's a euhLlety that are warned ate-nut whether nth-dent: muld n-nLice [we were prepared tn grade the prclhlem curreL'l either way]: exactly what happen: in part ill the Hiingnn currrer: ercacLly ECI hil-pninlci' la the Enterprise admiral-er]? cur nut? 'T'he Hugh-ch in "can take 1.15.1 tci ED hit puirrta before being deetreyecl" ie a little vague- Perhaps one ehciulcl calculate Pl'lt i=- Eii rather the Pi}! '-=- EIJI, cm the gee-uncle that till hit [mime aren't Hrflngh. T1: line] the anewer tn that you'll heee tci read the training ieahuale fer the Enter-pm; which Lurt'cirturretely are claeeiflecl. . . [Ne eeie enticed the euhtlety.) Prehlem 3 [2D lite]. De. any g-ieIe-ri. clay, Jane has in. her refrigera- ter her jailer-ice entitle: effiui-i juices: orange end-,J’nr eppte. Let 2': EJJLLITII'JHE denote the member of beetles ef Grunge-juice end ‘I" denote the num- ber“ ef betel-ea of eppte juice on any get-en. dey. The rebut-titty mmem of}: and ‘I". thlalgl, 1'5 gee-en try: Ila] F111 1n. I'..'1.I- their. DIE-F. marginal Iii-Ilnbutim I15" I marl .LitI- mm- glrull dastrEI'I-utmn I'JJ'. "I’. {11] Flue! .UIE EZFFEM'I'J: wnnlue I?! I. the emrtad 1min: I'I-_|r 'l"I mm: the standard item-nutty?! ufikl. [e] Give-r1 the: an 2 certain eleg- eh: hue m.- u-ppte juice in Frea- refi-tgeremr, find the emtetflity the: rm the: day eh: he: u: must tum butt-fie: LII LII-mtg: flu-CE 1"“. her refiegemm'r'. {:1] Feared '.':I':I-'.'|'.l".'~ 'l'"|. Sntutmn. Ila] "Marginal dintrthutinn" jlmt means: add Her. raw: and Itlfllllm I'IrI. Here they .111: 3': III- II v II II | II we Separating then-I nut {which _'Irn1:I wnrcn't. Helen-r] [In flu, but. :Il'. malt-El: Ll'Imy. clearerj we have Ieznmpuind the distril'IHIJrI-n far K? —II- I and fer ‘r’, fie] En wr. can :mmpute the mean her I. LIHI Int-flli-JHOJU | jaflfifil the mean of 'f, .EJIIIII. Ef‘r’t =IJ a: filIJl 1x LIED | 2 x ELECI = [.60. F'Ll'lfl]l.'_|.' we. (Hemp-111.: |.|'IE variant: n! I? 1-' x can I 53 9: eat — 21 an that. fly: = '-.- Ii".._' = (133.? be three declmel places fee meme-eat}. While the teatleeek Heme te- pretet' herleemte] tables te em:- teerlae the prebeblljty diatdhutten, wrtecet tehlee are mere cenvenjeut fer the user, meefly because we're need be adding cutemm ef figures. (Seaside: the pmhlem ef {unrelenting 5er and In. for example. We fiJl eat the table as fellewe: ex In .- Er-eLu which we reed ed! 51,; = FIX] = LE and Fulfil] = -1.:"|.'|:, al]r.I'III'I.ng In: [D cmnpula: “I = ELK—I: — Iai- as aha-Te. 1I.'Irl'.'l.j.' Iie-ee the bee]: prefer hefieentel table-e? I‘d-e deuht he- ceuee they use leee space when typeset. But where {ML‘IEtLiEI‘JL fer the pub-Ileher they be very djfierent from whet’e convenient Em: the student. BDLIJTIIEIHE [e] "I" was the number at h-ettlm ect' apple juice, and given. that the hat he apple juice an a given eta].- meane. that. we‘re an the first new at the table: -Im I "I’LL meet him" h-nLl1rJI nr aennge Juice 1T.ea:rI_'II K ‘1'. .1. Se the answer 15 the Jump-urban hr the sun: 111' the enL1-ii-J: Mr K = 1 11.1111 I = l in new 1. ee'lati'ne [In Lhe whale 11:11.- 'I" = CI: , hers I e.1 en's ,, pm e 1w _ m _ —M _ Tl _ e..¢..—.. banking at. it. art-ether way. P IIH '2 illicit“ [Ill PIxe2|v=gI= MED: 41:}ij LL] I3.IJ?5 I I11 I 3.91:1 =u_t?5. Hut Lhe eammnn-eenee inlJEEPTELflllIII'L—th'. ElienL Date—:1: |i1-:el_-Ir Ln stay with yau infiEEl' th 11.11 this ane. [Much he il waule] warn-I Lhe ea-elelee n1 nI.11' hem-l1: [1.1 have 5111.1 Tememh-er haw tn the the sentinel I:.1]I:I:I]nLiI:II1'.I 131131315me badly. we suepect you waet'l.) [cl] 'T'hie part :InunhIL-J: the n'mL week fill the who]: pmhlem. 1.7.11; ail-511 the easiest. way ta eampute eaverianee ie by the finial-Ila Dewitt}: LIF'ET'I mull-r. and if we 1:11.11 Lhat hen:I Lhe exp-enlath HEY] l11ena nut [D be lK1KU-15-1fi13{fl.1jl1!:3-3'42'113- |lat]ant-MEIlelxflflfilleleflfll‘i, which hem-1:5 null. la 1: :Xf'l = 1.515. [Ha-here lhnL there'e nn paint. in mmpulmg the eantril'mtinn l'mm lhe l11'et raw, since Date 111' the mu1tlp1iere in filer-13': Theeell'aee Ea'i'lx,‘r’]=1.'1‘5—TK 2 = —fl|.|J5. Hawmmr, in. thin ease Lhe l'arrnu1a mutt; = Eu. — mm — mere: =11H‘1" = 9]] "I'll [which it the actual defieitian at cataflance] it a Little leaa week, meet];- heeaue 1.13.» and he happen ta he integere. First. we hufld the tabla: far 2': — he: and "I" — 5w, 3": - I-lx Ilfllnil III I III and new the eetarianee eemputee te L1nu[}:,1f'1 = [—1: .=-! :—11 #:1113175 | 1—11 1-: I xflflifl; -1I[1Ihfl-rlfilfe1xfl.filfi {IJZITFI H.025 [LL15- - ClJJtfi = —IJ_IIIS. There’s leee arithmetic in this 1.I'ei'ai-en. but. when knew? if the means hadn't turned eut he he ea njee. there might have been a let there. U Prahlenl 4 [3|] pte]. [a] Amy-34:} tee-net tteehe ai-Ia-a'tatule, ee- aett-tl fear steehe have prices that at“ thereaee tn the nett trading pen-ed. An tallest-Jr eeteete ten atettnet eteetn' at rahae'rh withaut replacement. Find the pretath that ee- aetl-tl three of the seleeteef ate-eh: have firteet that tie-II! 1'11- ereese th- the fleet treat-115' pm. {[1] [he :15" the .313 flaunt-1 it Help}; stuck. Emth trading pet-tad] LL-I pnee has: a: chance :1}: men-earring. in 1|.1 trading pe :I'IEI'Jel‘JI:J find the prahahihty that! AAPL- 'sr stun-.11: 1111.51! increase: 111. ezaelty n} the herding reread-1:. [L'] {Reflean tn part In. [W treating _i11e1-.1.I'.1e1'_-:_I find the It: pasted value and: standard dntutiun. uf the manta-1- 1" uf trading yin-texts in. which AAPL-‘e :tael': price Wmfllet. 0:1] (Rajah-tug tu phi-t {It}; 1‘11. iflfl tasting pet-texts. fimt an up- pmrtflmte pmtatflity that AAFL'e stunt: prim: tm'efllel in. 3-3- tel I35 pet-teat, fiteIttJ-ttle. BDLIJTIIEIHE flotation. ta] Thin ie a hypchcotoctIic piohlcrn'. thc laIch population. in. ie di'l'i-dfld hctnrccn thoec which W'iU incroaac [-1] and that: that won't [.26]: the Eflh'pflpulafifl-Il. 19. in divided hctnrocn thoec 1which W'iU incrcaec [3] and thoec which won't [F]. So Lhc an- ewcr in out: _-1xan3uu _ 16:: it] _ nit-15m ‘ rezr' Rounded to three decimal placed, this in LUIS-t1. {h} Thin ie. a binomial prohahilityr: 1J= H] (a } n LLEE“ K 031" = 111:} it till-165515 at dJJl'iE = $255321. 'r'nn'rc cu ppmucl tn Tnan lhiJ: to 111'“. [c] Thin ia the alpaet-ed value and attendant deviation of a bhmtuial probability Iwith r1. = lflfl and p = 115: n = rip = fill. a Rim .fimaacxon «El—:1 r1.t'E~'tE~'t. tI chi-mid he mat-lad 1.1: “1.399. {d] We are aching [or W55 '1'. it: '1'. {FE-1. where I :L-: t'flflflmifliiy dih- Lfi'hulnrl I'JLI'I mnan E-Cl and nLandaTt'l dniiaLinn. 41.39393. 3-inch: it ia approxhutely normally distributed, we eetimata thie. ae. FfEEE€K€EEI=Ff—Efix—Eflfiij =1: 5- f x El] { EI- ' -i.E'r"E'r"E flit-"HE’S 4.5?5'ttfl Lei-1: LUEUEE *i .v'_' «11.02063. WI: cetimatc thin as l 3-: PD!) '3» d '3» ffll'l i'. 3-: {1.3461 (3.69.2.2. which mun-r11 in {3.592. 'T'I'Incn who: know lacu- tn lair: ill: aninuity mrrnctinn—JL waan'L requirnd—wiil 5:1. .1 I11an accurate alumni: PIE-1.5 -='. I -'.'. 65.5] = P[—E.5 -'.'. II.” — ED -5 5.51 = P 5.5 __-_I 5': ED 1: 5.5 *131'1i‘fl'tfl int-'33?! 41.493533 P[ 'I at: .i at: 'I which, if we appronituate h].I 1.3.1. yieide FI—r..'.'_l -=: 1:; 1.1.1] = .‘t 3: 13.3.5315 = LLFTFEL 'T'I'Ir. actual vain: in HE E (1WJfl.5ifl.-t""" i=fl.I-'_1-ttl1?_1, L i er. fine: again. the continuity correction taluc [QT-’3] ie clcecr to the true anew-tr {fli’i‘t} than the uncorrected value [0.692). U thhem F: {31] late). A rmflcutur acuity amepapar ii define-11d be- tween. 5 1m. and 5:30 dm. The tan-teal time, it {tn EH13 of min- utes after 5 fl.fl'l..__.l_. of the headphpar he: thejultuwiag- pmtatt'tt'ty dam-ity function fit! .- 1—1,Ucec2 fix]: .3 III. xiii. :bl 1: {tons of minutes after 5 one.) [a] Find the probability that on a. randomly selected day, the mapeper wilt ante-e ofier 5.15 1111:. Co] Find the enemy-e meant time of the mnepeper. [c] When. ehouid a. feeder Ioohfor the amped-«er. in. order :to- h-eilc d ‘I’Eu'i’i. chance that the leaner wilt have arrived? flntutmn. fa] 5: 15 ie 1.5 ten: of roinutee after 5 : tit}. Accordingly, you are being eel-red for ‘1 l K I at ' 1 Hath-11:] |——£t1={:t——:| =—_. LE 1'. I '1 .5 H:- ‘r'ou don't have to do thie by an integration, ofcourae; the an- swer ie. the area ofa triangle with here U1 and height. til-III = Uri, hence in 1 r 1 1 f 3"“: 231:“;- BULIJTIIEIHE Heurrnied, the answer is 3.331, but this it subtle: the exact answer is 3.31:1le but the: rule ie “round tn- even“ when the last digit is a 5. sn- vtru round tu- thIJEl [rm-t 3-1333}. {h} The average arrival time of the newspaper is J lit-11:33.3 =J1— E: 1:17: n:- a hut this is. in tens. of minutm; se- the average arrival tirrre at the newspaper is 5 $3.33? it. 5- .' U3 : ’13. The physics art-:1 mgiueering mature amen; vim—wait, what are TUE-T lining amen; veu'tt—rriilremgniee that the neuter sf 11m eta tr'iariglrJar tiger: [matte at a unifermJJr dense material} it lecated at the average at the three vertices. 111 eur case that. are at Ifl‘m, [1:1, 11, and H.131; 1.31115 1.31: Deni-er at 11111.1: 1.11 at “3.31 I |IJ.11 I 11,-:11 If}. 1) J ‘3' E ' The r: cemriiaate at this. is. [1“. This rule tar flhdirrg a eenter hf tututt only well-3.13 far- tn}- ahgtea hewever- It dewa’t Ivaelt tar quadrilaterals ar higher- :rrdsr pelt-guns. These are worth learning fer physics anti engi- neering majars. but hueirrme majere? You'll never eee it again in your ]ifs.. . [:1 We‘re: melting,r fer the value: at e se- that Z' ." Ii' J f1a1dx = 1:11.93. a i.e.I E L 1 — ex = 11-515. This is. a quadratic equation, :3 e— — = .‘t‘ I I! «'3' 43 which 1111-: 1.1-1: sI:|\]ui'i1:11:1.'I:I 1.: = 1.15 and 1,! = 151. tilriiy the first rs meaningful {between D and 111. Thus the earrert answer it 1.13 Lena at rta'rrutea after 5 : IJIJ, i.e. Fr : 13. Pruhlem Ii {ED late]. A Jul-Hey me duria't'tittett tu firearm-e the num- ter a! harm-r pn- weet: adtttte tn. the Untied States mend. trfl. hen-1e magnate-re. In. the rtu-tleyJ the HiaI-rter a} heart: war ram-malty 31:3- te-theitectI with a area-r1. an} 1-1 hum-3 end: a rtanttar-et detltflttafl a} 2 hue-we- [a] .3 rim-my pm'léciphnt tr 111.1131:me selected. Find the pmtu hrlrty' Heart. the 11.th 1131' .311th .rpmt. an. 13:: hum: mutt-.3- by the partiame tr bet-mm 11.5 and 15" hum-3 per urea-h [1:] firm- eta-trey partiatpante are raudumty sebatedt Find. the yehahflfiy that their avg-age number uf hum-3 per- week spent an the heme Eurnptlier' £3 Legs than 1.1- ham-3. [1:] Five na-uey parttatjpahte 11h: tandem}; reteetett. What ta the What-they that amen; these five turtle-yea. emaetty twe- epe-rtt between. 11.5 and 1'? heave per was]: en the heme enm- pater? Eaten-m. ts] ‘n'au're being asked fer 13:11.5 -='. h” -: 1'91: PIf—lfi 1': ht— H -='. E: F —1.5'_1II—1r1!:E 2 ‘ r .1. = F[—1.25 it E -=T 2.51 =PI'IEI:.' 3:1.31- Free 231.15] = 3.31313 - 13.3944 = 12-3331, which reunds te 121.333. [1:] Leti [x1 I It: - I; I half-t he the averageetteur randomly selected sum-,ng participants. Then HE] 1-1 but mm trth 1. '1'hus PE +_- 12.1 = Fri —1a1t-; —11 =P[?r..—|'| =fl.fi—P:fl~:?~:II 121.5 0.1111 3.1533”. That mun-3s te- 3.133. [42:1 Freaa part {a} we eee that the ]LJr1:1t:1a1:1il.1't;|I 15f true epeiuiieg be- tween 115 and 15‘ heart he the cheep-liter :is 12.3332- Therefere BDLIJTIIDHE the probability that ere-:tig.r two at litre will do this is r ueeezlur r re‘ = eun rounded to three decimals. Why did we nee few decimele in the eaJeuJeticnu? 1I'll'auld it have made any difference if we had used thrre'.’ U Prnl'I-Ir-Tn Ji" [m Jets]. The time required to enmptete a deter entvy in n ant-titular terminate-ind recruitment; system is an fipuflertttnfly dieb-itnted rnndnne unrintte with e mean e_|' i: nannies. {a} Find the ere-tetitity that a Pendent-t? eeteeted data entry unlit be completed it"tttl-‘til't- 1.6 minutes. [13} Assume that the seq-Miter ej‘ time-5 between meantime date eat-rite tr- a sequence at independent and identemlly dee- tfitmted ezq'atnentiut runde marinate-t. {I} Find file upeeted t-e'rt'ue and standard demtian a)" the number. it. at entail-.1 mmpteted within. .111. H minute reread. [11} Dr]. an. aeealrmn when there are fine entrta-t to lie in. put, find the pmtutlttity I'J‘rat exactly entail-.1 mitt be cemeteted within an 3-minute pet-ind Satutmn. {a} The PDF efan eprnentiaiij' dietributed rauderu variable in at the farm in: '1'”, where the meen trelue ie Uh; therein-1e e: thie expmientielly dietributed RU, we have it = h": [date entriee per minute]. We have Pix-:11 1 u ’“ =l—Ir Eubetituting l = LE we get Pm: rat 1 r H 0.551. [bj Since the timee betttleett treneeetima ere eitpe-Jiaitiaiiy die- tributed and independent, the number nf time-em in any panic-ale: unit at time ie PeieemL-dietributed- {i} ‘r’en’re being eelted te epecitjl the unit time hater-val an E minutea. Since an average I minute; are required per traJnIattinznriI this mean: an average at -l traneactiene. will be completed iu .5 miuutm. If 3': deuetm the uutuber at traJiaactiene. actuaiij' completed. thetefiere l: r] (1;. P|K=h1=Er~ *1. New at general. it Alt '_ I_ ...H. Heme—EL , the mean at I in 1. and the standard deu'ialtnet at I ir. HT. tn flat-.1 curse, ll'.|e'ri-.lir.|r\veI the mean at it: in "l- [wl'mzh melee: sense: we said we avenged -'i tranuetinne per 3-minute perind], and the standard deviatimt 1': l = fit] From the teem-Ida [1]I we find Pa“ =51 = t = gt ‘1 afl.1!—iE tn three decimaJe. [Either enettrer, te- three decimals at are e retienel multiple at e ‘, wee. accepted.) U Problem El. [212' pie]. In an. attempt to TMIJ-E'EJ-Tfl the yestetian peril-Jud all: J'le:l'l'\et_-:_I thirteen femntee were abeerued. The gattntta-n parted: _|"ar the-re 15 fen-eaten were fauna! ta he I'lfl' '13 '13 I'll '1-3 '1-3 '13 ’13- ’15 I13- r'lf'l fill} 315 days, t'eljtect'ttlety. In what fullernle, it my help if I tell gnu. that L a = 55; and Ella — E]: = name. [it] Find the mean. E and the eanlpte standard deniath 5 a}: Hui-r Jamqate. {11] Find the Fifi eunfidmee interval: In:- the art-teen gestatinn pet-tart r.|-_|r fetfets. [e] Later it ie deiee-mined that the aimed-d detentiern uf a: geltrltticm pet-ind is netudiy e = Lt-‘Er deryir. Find a: ‘fi'fi eumfidenee intequ fur the enenn gfltntinn per-ind neiag a: ate-tie date and this mine er a. BULIJTIIIIIHE flotation. Actually. the mean geetatton period fiorferreta reallyte about 4|] dare. [ know thie because [once loaew a couple who owned a ferret. [Which la now illegal to the State ofCalifoInia. incidentally.) he. fa: aa l'In concerned. l'cl juat aa eve-cu own a feral rat. 111 Lhe PILHL'IhEEI version at [he exam—the exnrr. nuctuaili}I handed mat to etudente—there tree a lutepl'itfl: there were 1-1 data items instead of ll Students were inetructed to remove one of the dfi'e fifltltl. the [let [we’ve already done that fine you in thie eolution eet]. [-Io1:|.l'ev.'e'|'1 thie was oor.|.1|;..1letel].I irrelevant: all that matters is the ammo E‘- K. and Let. — 31-”. fa] The mean ie. given by — l X=file = F = while 1 r — _I .a- = n—1 :01. — :-:1 define = r2 = 4.102551 Therefore 5 = tit-'1.ltll.'-'_'iT-'=i-‘_E|25 ln three deeinnaels. {[1] Fi-eoauee we have .1 .compte ntae-riar'ci deriatinn, and unect the I'L— 1 in Lhe dEflDmlnfltflTl we :rr11.|.'I:L1:L-:e the t-etatielle. 'T'he 953$. confidence intervel 'Le therefore 5 GE Looking up in the l table we find Laggth = llF'i‘. hence the confidence interval ie 42315:: = lllrl daye. i.e. between rll .233 claya and #1656 clan. [c] [f we actuaJl}.r know -:rl then the confidence inter-rel is obtained ueing the normal distribution. and is _ cr 3": : Eeeze fl. E = Ln n.1.=._l.1 i.e. earn : we: a. 42.152 : the am. Prob-Mm Er [2:3 ptej. Moeeryhim' Auto, the. etaime that its: cor: from. the totem model glee-r eon emetehate fium IE to 542 male: per- huue- tart-1- rem-ode or less. rm. tree-rage. Cor-mm Magazine decide: to tat this new. Ely moderate-those“ Meet-refine from. this wee-r. Shep-pose the oue-roge III-Evil time for theee 35 core times ta J1.l eece-nde. with o eon-tele etohdord deert'o-t'ton of Ell-'1 seconds. fa] Foemutote opprop-r'iote emit ohet the-mottt-e hypetheeee for the occeterot'tort times of the core. {to} Cheese oh opp-rup-r'tote test rte—tutu octet describe the rejec- tion. reg-ton fee" the 2.5% stgnfiticonce let-ct. {c} At the 1.5% etyntficonce tee-lei. shout-ct Gor't'ren-d conclude that i'l-[oeerghtn-t'c deem it fer-sci“ {on Horned an the oqapmprénte ottcclztaed tattltieJ find .111. Hater-tut canton-ling .Ltae |1 wotue. Smitten. [a] H._-. : u: -1 [or n ‘45 4}. Ha : tt 1;: "L {13] Since we are given it nempte elem-lard. |:i.etli.1'|.:|or1I we muel one the 1-teet. That lTll'.i‘LT.L'i we uee the l-nlattntic. The :rejeL'l'iocn region fine the lj'lt eigniflcance level ie l 3* le.e:5..!e = lum- [L'] We compute the t—ntnl'iettl: h]- Jt HI: _ -t_r -1.tl| _ as.ch deeds—e 1 = 1.5. Fly Lhe :rejeL'l'iom. rule to 13an {'h] a'ho'deI einLe 1.5- ;: lam. we do TejeL'L at the 15% level. {on “'e reproduce the entire :row or the L—eutan table for .35 degrees at [rm-loco: IEIIIEEEIEEIIW | BULIJTIIEIHE Wke’re ael-rheglr which entrjm are araaller than 15; fie: theee which areI we can. reject at that level; far thaee which aren't. we can’t. F'ren: the table we eee that we can. reject when at = GUN, but we can't when at ewe. Therefere the :p-value h'ee 1.11 the inter-raJ IUJIIIIISJJJIH I. h eaJeuJatar er eemputer wachl alJew ue ta: eaJeuJate the exaet p-t'alue: p DJIIIIISEES. All we can aa1.r with the siren tahlee ie that the p—value :ie eamewhere between CLIJIJFJ and H.010. U le'rtnm 'Itl [it'll ptaj. ..Il. researcher Tart-thee tel test the aerierlmn n}: a partith .Itualent that at. learnt n}: alt entleye rrhrdenL-i tum-dell prefer net .te take a. etuee that meet: earlier than. l-fl e..rr:|.. Fee- Htie puma-eel the researcher ennal'ueL-I era. apiemn pal“: elf l-flfl rendeme selected rind-eats. [a] Farr-mutate apprupiaa: Hall and alame hypuihetfl fur- atae feterll'flfler tu- are. {h} Cheese ea. apprup-tat: tat flaitette and deem-ite- the rejec- t-te-a reg-tan far" the rl‘lft. significance lie-met. [e] Let K be the fltfll’t-tlfl'l“ ru' etudenie who aartirtpa-t'e in. the eta-we pelt end prefer net in take etaeeee earlier than. H] era. Fame the mammal value elf}: that aller altaw the reeearther :r'e- reject the et'uae-rtt’e eeee-rei'an, mtg the test etet'tettr' a-naI rejerttan reg-tea 119-1. {tn}. Settle-en. Ifa] He:p=tl.?aIHn:p bill-flared Hr. :p-eIJ}- Weuee thje [annulafiart at H" heeauee it'e. {tear tram the {flrt‘tEIt at the problem [eapeclaJh' part fell that we dauht the atuclent‘e aeaertien. [h] Thje la a hmarajal prepartian prehlera. an we must uee the .-'_' etatjatle. We eetapute a = ear — [BIL-’11 = ~,.-"E|..?' x Darren = emanate, and therefore _ e — a. a _ ue-eezee' The rejertiael regjael le 5 -='. Ric-eh hut in “q in net are at" the standard cutaEEe we uee; we'll have te earapute lt DL‘IIBEt‘J'EE. We're teat-drug ter a value e an that PIE :a- al =l}.IJ-1; which mean F'TIJ -=T E a: e! =fl.rlIE-. e = 1-?5 eeraee ]:Irett:.r elaee. heeauee PUD «’- i ‘45 LTEJ III.-’15':":‘i ee we’U take in .14 = 1.?5. [Ta five rie:::l1:l:|aleI the actual value ie Zea; LTEUE'E". an this is purettq.r tight] Thus ea: rejeetl-eu rule hemmee Eel—lffi. [e] Ea we wequ eempute & m“ ‘3'? . and eheelt far i e. l.-'"."'J. ..I _. Tl‘u'e t1anetatee he 13 e: I1? — LE 1-: flfll’IEfiI-L-‘rfl = Chili-WEBB. Ejnee I in the number at etudecnte. we have 13 ENDS; and therefare e111 Iejeetjrm rule tranelatea ta: it -:: El .9305; m trill eta-dents repeat that they dae't lll'lfl takingelame Ihel'i'rre m a.rr|. we'll reject the null hypntheem; that at El repnrt thatI we can't reject. El in the maximal value all X whtel'l amulet allnw the reeeareher tn reject the student's aetertaan. U ...
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  • '06
  • Haskell
  • standard defiant-flan. ef, fleet tree Lteee, standard deviatinn cell, standard dfi'n‘lit'lfll'i ate, o. pmhehtfihy tree, tn three-digit accuracy

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Final Fall 2006 - FALL HIDE FINAL EXAM SflLU'I'IDNE MATH...

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