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Midterm 2 Fall 2005

# Midterm 2 Fall 2005 - EEGDND NDDTEHL'L MATH 31 NOVEMBER 9 m...

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Unformatted text preview: EEGDND NDDTEHL'L MATH 31! NOVEMBER. 9. m Problem 1. {1393'} .4 l'uher eeife when. {“5an met-mm. gm?) The tuber”: mufﬁn pmﬁl jinn the eel-e of when in Why mmm HRH-ﬂ mofﬁﬁ'ﬁﬂﬂmﬂa ehndn-rﬂde-rehbﬁenafﬁﬁﬂﬂ. Amwher msmamwmmmmwwjmuLEmm elundqmdl 41mm of her annual eel-ea. Him.- there are [E marlin: if! e. new :-e 3.1th lfIh._.,_I'];delmtetheeeleefarmemﬂhdmmrythm1lgh Deeemher, end I ﬂeuntee the amine] Helen-1, then X=IL+---+Xﬂ. ‘I'hereﬁnre E{Ii=12:-:EI[X,}= lﬂxﬁﬂﬂﬂ=m ﬁx - ﬁxcrx_-Vﬁxm=ulmllﬁ. El Problem El (15%}. Sum-we that e. I'nhrmmui eme-rime-mt t'e mm with 11:21] Weldeprnhmﬂﬂy efmeee efp=ll.-i. Fwwuhienr if I dermiee the eumber a-f we. ﬁnd FI[Q E I 511]. Fan. will do \$.41!th mum. {in} Carmina Eha'e pmhihiia'ry 1.l:.'i-1I|'I.§I the table nfhinmrdel pmhehil- ltiee 5mm a! the Met 5} the ere-1L Dan‘L ferget theme ere hinﬁtdduel pmhehdlitlee, Pfl' = H, but ulmlﬂetive HI 5 k}?! [h} emu Lhiepminhﬂ'a'ty wring the ME WWe In the Hemniui, wlthuut. :Lhe muliuﬁity mmﬂee. [e} Estimate Lhiepmfuhﬂity Ming the eel-null wen-mm m- the mm; min; iI'JIe mntinm'ty mm ILL?! ILLE‘. -:I.:I IiI-IJ'J'ZI III-I35 Lam. I] EA. ‘I [.5 LEI LIL! III 13.1 FEﬂURE l. Bjmmiel pmhnMIiLl-ee for r: = 213, I? = [Li :9 5 It -=_:. 1]]I wltJ-I untrue] mule miner-impaired. {e} Leaking er. the p = {H column at" the tehle, we ﬁnd Pu: = u] = 0.159%; Pix - 1m - ﬂ.11i'14 Pu: = 11] = 0.07094 Adding theee remllte In HEE’ .FL' £1]j-ﬂ.34?31". This I'm-ma is exact [tn- Ew. decimals}. {h} WI: cmrmtl: rr=np=2ﬂxﬂd=ﬁ e: W=~Jm=meﬂm New Hempute. m the mntmlu'tj comedian. HEEK‘EII]=P[1‘EI—BES} 1 X —3 3 _ Ptamme 5 2.113039 5 219039) = mum-135 5 z 5 1.35931} = ewe 351.:mmu—em 5 350.45.54.45] = l|2|.414£'|-4£| — HATES? = 0.23353?— Seﬁeﬁm- III Figure l wehaw the her-chm DI the WHILE far I = Q, I = 1II|I1 and I = I]? together with the rim-me] dletrihutlnu {the thick mIn-eﬂl having the name- meen emi etemlmﬂ deviation- Thin :elenﬂatiun le met, and in. mmputed Ming Liammmtlee [you tank] elm} camp-ute- iL tuning a eel-mlemr with utetietim] flmetinueﬂl. Ifjuhu ﬁrst. rmmd Le hm ﬂeeimeh: and llﬂEﬂ'IEtﬁiillll-ﬂ, your ere-Ind get = Fit] 5 3:: 1.33] — Perez 1: '14er . ElAHEE'F - Dem-u . meme. Thin mm eeeeptnhle. This elﬂenletien ﬁIet FEHIJIfhi 1.35931 to 1.33. deer. the table leek—up: munch: BABE-1 te [IA-E. ﬂeet: the table Joel-mp: and Mlhtreete. Thereeeememtedwnytnemnfmtetrmnthetehleeiﬁtede linear interpeletien. Hnﬂ eetimete PEI] E: 3 ‘3' Mile-Elﬁn :5 [1-11-1543 PEI] g: z 1.” 0.4554353 Fe muse-17, He that the difference it [IL-1 HIE-15 — ENEH? = EIEEEED]. Aiming Eur eetrn ﬁlmy 1H- e wante- ef time here: whether 3011 get [LII-“i" er H.239. the enamel iii [“ij fer Elem the true ﬁrmer Ila-1TB? of part {H:I. The exﬂermtden :ie in Figure 2: 1we‘re mputdng the grey aree M HI'I eppmﬁrrmtden tn- the Ieﬂ area [if you‘re ﬂeeing thin in enter]. enﬂ it"ﬁ j1uit nut very eeeurete. E 11.! DJ)? El [.5 f l.5 Lﬂ Lﬂ.5 11 11.5 Fugue: 2. The ere-a under nee-me] curve {grey} with- e-el eer:|t|.1iL1tt_I,I eerreetlen h: net n. my gee-d nut-preki- metieh te- tJieere-aefthe red here. {e} With the henttmiity e1e1-1-enethz1t:1 thiegem-e ten-eh better; ere-enm- pute Hegxgm-Pteegxgne] =P[EL55X—e-=_:3.5] _ '11 - 3 e- — P[ﬂ-2232 [B E ilﬂﬂﬂﬂ ‘5 LEE] . Ptee 3e Item} -P{e 5 3-5: 13.22.11.113] - [IA-Q4925 - EM? - 13.35%. This eemwltet 1min; the Full eie-deehrml [Ilene pee-jinn: the mute nurture: h: = we 5 31:].en1— Hue: 5 0.23} = Eli-HEW] — ELDER-41 = 9.354347". UH hr nhmrt four unite :in the fourth deeimel plnee. hut quite weep-table. IThe answer ten pert [e] i-c etill eheut TE- tee- high eerepnrerl be the exile-t melt elf pert {ej- The picture minted With the enleIIJrI-tieu luring the Denti- 11I1ity eerreetien h: ache-urn in Figure 3- ﬂ.l15 D. L5 ELLE. III-II III-'11".- D.Il5 II .1125 El L5 i iJ- 1H?I :ID.5 LL LL!- qune .EL. The area wider the her-me] eiu-ve [myi with the eentdmiity hen-eetierJ—ie., mtemiing NJ extra 0.5 nnlt. th- the left end tn the right—ht :1 M11.- gee-d mewhnetden tetheeteeefthe red hem. Another picture, himiler te Flgllre 3, EIL'IIII'JHH-imt the Mereneee he- tween the here and the mantle] eunle (in yellow. Hate that the vuinnee e2=2|JHELI1KEIJE=I13 |'.I.3Il ILL! ILL: IL!!! Fttrunr: i- Yelletr are-em. rega-eraeut erred-a when mlng nnrmaJ ennre inatearl ef hare.1 with the mﬂlh‘llliltj' enr- reetinrt. is leaa thnn the nrle-nE-thamh mine of 5- erh'Leh 'ut rennmrnenrlerl he- lnre mine the mutual appreethnatlen tn- the hinnmial. This: be why the nermalnapprmtimatim value he about TE- tnn iner- El Problem 3 [15%]. In henna-drum with the when nj'ae-me aer'amni- egchrte 1|.nt aheii meal-ire that euthanakee en r1 perm-nim- aeeﬁen ef the San Amer-eat jhait ﬁrm:- a Peter-ea mater-intent, with an. average nete n-J' [artery '33 year-r. {aJ (1'13an that en- that election nf the San. Afr-life“ Inﬁll there hen freer: 1w earthquake far the he! 31] yearn. wit-In! in the pmlrar‘eliﬁy Mtheneﬂnnemﬂlmraﬂhtnhheamﬁhﬂmm? {hj “he: :‘a the whim that at let-let 2 earthquake: have nan-rel: aim-e Jenn Heidi-tin Aura Wallet threw Smtﬁem Gilliam-1h in lT'i'ﬁ‘F' {The waterline-I1? £1 amt.) Sela-Em. {a} Thia can he arm-tiered nae aft-ale aura, and we‘ll dn hath- Firat nnte that the 34] year ﬁgure in a eenlrﬂete red herring: whether one will e-eeur in the meet .54} year-a ia a'nrieﬁearieut nl whether one neeurrerl in the gave-alumni JD. Thia Ea nnntained Iit'ithin the deﬁning prep-ertim of a Pnirumn [ante-H: the liraihrthilit}.r at an [here .‘4. = UTE. nrre earthquake ever-3r TE yearn-t], then Pt? 51:] - 1- 5"“. Saying that one will happen withln the next 51] year-a in ernlim- lent tn aaying that ‘.r" *-'_C El]1 and the eerreet anaaver ia therefore l— ﬂ—tem = 0.13??— Altematitreiy. we ehange the deﬁnitlnn eE "unit time” 113' reaealing; instead nfaaﬁng that lf'F‘Sel'an earthquake happen}; e'I.=er_I.r year. we any that WIFE nfan earthquake eerura every El] years. If I new-lienetet the number etear'thr'ueltet I'ln'eh nut-ear in e Eli-1w rental. then * 5|] .1 FLT: a] = Era-'1 :a: ﬁll- And are are aalring [er the [unhahility that nne err mere man in El] yearn, Le. in-kJ-l-PfX-ﬂ}. k-J But FLT - El} - a‘mﬂﬂ. an we get the aarne answer aa before: 1 - KW" = 0.13m {h} Thia ene can e-nljp| he three by remaiing: it haa heerr 23D yearn rdrree ”1'5, and an are me the enmtarrt RBI] *— a earthmlaltea ever},I Eli} fan-a (and let A: deante the runuher et' earthrplaltea hr 211:! yearn}. We are aekhrg fee- P{x:_=ep=1—F{x=m—P{x=13 = 1 _ r—Jt _ Aﬁ_'ll' = 1 — r_mm — %a_mm = 0.793%. arrival h: a time pet-led rlenera'la nnl}.r en the lmgth nfthe time perlan nnt when the time perinrl enema. in the iirat nrethnrl, we- uae the fact that the randnrn I«ar'iahnle 1" 1a'hieh repreaertta the time heal-teen whine-thee ii eat-unen— tinily rltatrihlteli: il All: _J. HX=kj=Ea , This Iaelriem appeared en a reeent ﬁnal exam [Frill EDD-i. I l'Iel'Le'Ire]1 Irhieh 'r-i the term] included it- But part {In} his l'aa'llJ.r phraaeil: ene ahenlrl never ml: the prelarhliity nl anrnething amen; .lunr' hanpeneﬂ: it either happened nr it didn‘t, an the [arelaahliitjfI ha either 1 er I}. le‘mhliilij' h: aim-aye pneﬁetr'ue. In thin: eaae are can wear-rel eut hi it by argnhig that are mid ‘en a particular aeetinn” hi the San Andreaa larIJt1 but didn‘t apedfy whlrh methin- El Problem I {UTE-:1. The might 11f the mmmt Fill-lid in 11 “EH-11mm tug" Fawn-nutty Mhtmmﬂh 11 mnjﬁﬂﬂ made 111.11“ Honda-ad due-lamina of 114 mm. {11] Fin-It the pmhﬁhﬂi—ty that 11 Miami” nﬁmm tug weigh mm than 51 flaw-Ida. {hJ Fin-Ii HM: 95th [harem-I113 ﬁfth: WWI-ta af Hm tram: rim. ﬁnd that might 1'11 an that H}: 5' 1'11} - [LB-5. 311111111”. {a} P1}: :3 51] = 111;: — 511.23 g 11.11111 3-33.33 '1” _F( 111 3E) = P12: 2 1.1125} -%-P1[CIEEEL921] = llﬂi‘i'l 15L [ll 312111 11ml 1-52 iurI-tunll at [£925. NIH and “It With llﬂi'ﬂiﬂ Which i1: l'l-l'i'lil mthHEJ {h} Thu 95th wmti]: ii glucn 11-3 till: ultatl 3m = LEI-HEB- W: have 3' = [X - 50.231.1’04. 1-11: IlEIE = FILE ‘2 Jill-\$3.5] = P (—11: "HT“ :- 1.54435) =P1x—m23 a 11-1 1-1: 11511-135} = FILE 2 50.23 + I14 11: [ﬁat-\$35} = P111.“ 2 51111211217191. 51:1- the- 135th pumme- weight #1 E1 u1= 5111.39 gmlntld- El Problem. 5. 1'1 5%} A certain type ufiigllt hul'h Jim 11 am hn'giimm a-f i#1511} humming inn: bright-1m: 1111-11-15:: #11111: truth In huh'i, and the amudnn-t de1riuﬁan 1'3 51!? human. A mntmmr imam indies 1'11 Incl-raga? of 35,- mm ﬂue thmem 11m {ridge-eminent. {11} WmhﬁemmmHRmdmdmnﬂﬂenwmge twig-M- um 11!: manage afﬂﬁ' M11111? {h} “WI-11 the pmhﬂhﬁﬁﬁy that the mange m'ghtnm of 3'5 Min :21 T55 l-‘llﬂ'lﬁ'ltﬂ or more? [12} Arr: Him mm enact £111- We, 91- 11 ark-attire? Dali-cm yam- manning. Suﬁ-93km. in} The avenge [1:11ng in given hy- I'- IL +Jl:§,+---+.:l.";,:I 25 [in lament-whatever thma mat. and since the I: an: inrlap-m- flank Elf-X] =1t= TED Ilmm. 11' El] ”I" E ' m [h] We l1ﬁE| thus-ta I'lglmaﬁ in part. {hL We: are asking in: PRETﬁﬁl=Pﬁ—TMEE} T—Fﬁﬂ = ‘3:- P( It] _ I15) = F[3 :3 115} - lﬂ human". = %- Fin 5 2 5 11:1} = 11.5 — 11.191152 = 11mm 31:1- nhmut 31% at the package“ 1will have: an mange: hrightnam 121E TEE llLTI'IEI'Ii 4:1! more. [1:] Thain tabulations mllﬂ he met. if 1' man normally l'liﬁ- Lﬁhuted. [t “11111le he annually i'lilitrlll-lltﬁ'l :ifthenrjginal bright- ElEH‘iE-li were nnnnnlly distributed. But I Ila-Wham Hairl that the hightm war: EIDITEll'l-llJi' I'lji'ilil'll-‘Hllit-‘I-‘l. Thurs In: an: appalling tn thl: 131:1th Limit Thmrcm that T 'H Wmalrty "1:1:h malty rljs-vtril'altul. 31:1- [n] 'r: WIRE-ll but {'11} 'H DnLy npprmcimatc: the mudtn 1111:: mind- This: hm: Hath-tag to rln 1al'lth thl: ﬂwt that Ia: 11.11: mm ﬂinging. awryﬁ-tng bu l-‘lD With thl: original ﬂixtrthuta'm at tlu: lu-ightnmn. El Prablem B (15%}. A min-nit is tr: he taken for the ﬂat-i Senate eterittlmmthemteefﬂ'ﬂea. T'hepetiehnutd hemmtetnwi—ﬂﬂn i9mmyemmm'me9li'ﬁ. maﬁlienee. Theraettrtemteheun t'mﬁnl enmity eJ" EIEIEI madam-I5 selected mtenth'lt mtrre. and ﬁnd that 39-1 trait-end te wet-e fer the Emmhiietn mndnirite while 9T5 mat-end to write _|"r.II" the Rmhhemt. Fried the 95% mrIﬁ-Iierme truly-mt Inf 1:. the true pmhnilii-ity that unme- erae ehnmrtfmm the fruit Ninth-In 91mm te ﬂetejnr the ﬁemeptthti- eun. Hﬂ'llﬂ the mthtnre met the deem cmm afﬁrming 1|: mithm :I:9 mum pewter ﬁt the 95%- eenﬁdmm Emu-:I:? . _ 395. thtttmn FilHL emnpute p = E = Ilﬁli- Using 99% tunﬁrlcnt'l: requimt Ila-ting thl: tEIItIJE' 3am = [39995 [1min run}: In": 1.95]. Th: I'DnIJIIJIt for the mnhrlmtr. interml i-c then r e 5: 3mm- %. Le- 9.94 :I: [39996 3-: 9.99034? I 9.54 :I: 9.9399. 'Ihht 1e. a perfectly eeeeptnhle deeet-tptlen hi the eehliﬂehee imemd {tn rue}: to he on the mfe Hide, write it an nn intent-t], [9.5% 9.3399]. Frem th.1II.1t app-em the Daimfmhhcme: ere getng h: min the eIeethhh. 'Ithhig the :I: emu-nut teI Emu- deehnnht II: a little rIiIJy; tnre hr {at mmtll three deeimeh: h: mteqhete. Sim: thc Ilneu'tuinty in LII: ml“: nfp iti £459. nut £2'Et I'm. thc pull- :ctent he“: nut that the rI-ucigu u'itatritlu. I:I Problem 1(15593. Bthhm-Cetu mm- It em-Np-ﬁtﬁhg merthiee. Mirth ﬁtL-I Imminent Sail-hum Mitten with tut. tuttwrit ante-uh: whieh £3 watt-D- dtitn'huted with Wham mean and emu-tent dentuta'e-n 9.3 e: Ammme that 19 Mitten ere rum-1mm emulated amt meme-1'. run! it tin-rte nut that the merge Writ hf eerie £1: them :2»: 91}.[ﬂ e: {a} ﬁrm: the 95%. meﬁde-rmt inter-mt 1hr the W meme h. [h} Find: the 99% meﬁde-rme ﬁtter-mt Far the main-1mm men-rt IIt. {e} The 95%. tenth-deuce intern-e] again men 2mm = 1.959919. The eenﬁdenee Interval I.t"| then III. 3 =99991L9599E — TE he I iﬂll-E :I: Eli-399?. Again, the interned fee-tn in [19.99,9£L93| {rmthdhig te- twe Hig- hiﬂennt ﬁqu-eu}. [h} Seine prelim“, hut letting In”: = 9.5?593: 112nm— fiam}=eﬂhe:ee.t?taae% = 913133 :I: 9.193131 In internal I'm-m. this Iﬁ [19.39. 2412?]. 5:1 we‘re 95% eure that [9.93 5 f: 5 99.93 , end 99% eure that 19.99 -'_I. g: 5 919.91. We‘re mere arm! at" the heeehd ee'tirhnte, hut the heenmi eetimnte im’t me tight an the ﬁrat IEtIIIJ'IIﬂIE. Mae, there h: he free lunch: whet yen gem with one heed “1|th he paid by the ethu. El ...
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