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Midterm 2 Spring 2006

# Midterm 2 Spring 2006 - EEGDND h'ﬂD'IEHlt-L MﬁTI-I BIB...

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Unformatted text preview: EEGDND h'ﬂD'IEHlt-L MﬁTI-I BIB APRJL 'l", m Prnblem 1. (I525) An mute theater} neenhhty pmj‘it jinn-t. the euie n-J' newtsnermttyﬂetnhntetun‘hthmnfm andeﬂhndnrddetri- et-inn n-fﬂﬂll. em; hermhnthty mate-e rare ”dependent thinnghnut the year, ﬁrm: the me and meat-e de'lrihtien 11er annual pen-ﬁt. Set-Mime lfIh.-.,Indenntethe-eale-1ﬁnr the neentlutJammt-y through December, and I denote-1 the mutual HelenI then X=IL+---+Xﬂ. Therefore E{Ii=12 e em}: 12 x taunt: =nmm, ex - eﬁ rec-rug - vﬁx 34331::- 1mm. (Remember. the inﬂtnwtinm me that err-men: me to be given he he drain-ml phmJ El Problem 5| {M}. 51mm that h. tweet-at eaten-meat it f'l.|.'l'l_ with 31:24 Mandeprnhthﬂﬂﬁ efmeeenfp=l11 l’n-m'rnmiltenr if Idmnteehﬁennmherhfmmme,ﬁtdﬁﬁﬁxgﬂﬂl. I’ll-Hartline thhtthmuuﬂe. {e} Carma-rate thie pmlmhih'ty eaten the table efhinnndal [mutabil- ltiee. meme: at the heel: of the errant. Den‘t forget the-e are hnﬂvldnaJ pmhaldlitles, Pu[.lt' = 1:}, net mnmlative PH" 5 HI! [h} Euth'mte thiepminhth'ty taking the hen-met Wmﬁeh tn the Helm-tint, wltlient the mntiuniur mﬁettihe [1:]- Elte'mte thirrpmlnhtﬁty when the hermit Wmﬁnh In the himm-idL “Hing the ennt-innity m Sea-lathe. In Figin-e l wehew the harehart hi the prelmhihtee ftﬂ' I = IE, I = E, I = T, and J." = 5, together wlth the normal dJHtlih-ntlnn {the thick eun-eﬂl having the mme mean and etanﬂartl dee‘latinn. Ftuunn 1. Elmmiel preheldlitlee fer u = 2-1, 1:: = I13 (.5 5 F: -=_: E}, wlth net'nml untrue whet-imputed- {a} Lneting at the p = 0.3 enlnnn'u nfTahle 11 we ﬁnd HI = 5} = 0-] 1W3 HI = a} = mean HI = 'I'} = Ill \$03.!”th = 31 = meme Adding theae renllta '11 Fill: E X 5 3] = [LEI [3353. Thin anewer in etaet [to ﬁve deeirnahj- {h} We entnpnte 1:: Ftp-=21 3-: [13:12 41': M: W=eeuge [It in only «am ﬁanI emu-Ir: whitﬂI raw-rt he rounded to tile rleeimnlri. Meanwhile. we keep all the Freda-Gian we mm} New we enmpltte, mitheut the mﬂlh‘ll'litj' entreetinn, Pttgxgm-Pt-eegit-metre; =P( 1 {EX—12‘: 13.3} 2.24499 - 2.24499 - 2.24499 = PHD-EM S ESE-351343] -P[ngzgu.mnj+etngzgeem1 . 13.131921 + neat-1n - 0.4mm: Thin ealeiﬂatien le. elm-ct, and in. eempnted Hating h-Lithenmtlee [jun-n ennlrl alee :nmtmte it tuning a enlenlater with etatietieal fllnetiohej- [.wa tin-1t round to two deehnala and nae the tﬁhlﬂi [the procedure recommended [or me}, you Imould get = Ptﬂ E E‘Eﬂﬁﬁ] +P{El|‘3' 3' 5 {LEE} = meme + III—335% = memo Thia woe aeeeptahle- Th'hi udeulatioh ﬁrat ronhtie DEE-5343 to 0.35., doe-1 the tahle look-up: rounﬂe EILEITEIEIEE to H.133, ﬁoea the table lookup'. and adﬂat Aimihg for ettra menu-any 1a a waate of time here: whether you get 0.17555? or ll-t'iTEIE, the anawer in Inlaerahly I'ar from the true aoewer [LﬂlEEIE ol' part {a}. The etqtulnnation ii :in Figure 1: we‘re computing the greg- Hreo. Hri- ao approximation to the red area [if wl're aeohtg thia L11 color]. and it's just not 1.I'erg' aomrate. FIGURE 2. The Hm unﬂecr nonnoJ curve [yr-w} millil- mtt ooothtlu'ty correction it not a very good H-[IIH'EE'Ei- motion to themoftho red ham. [e] Witt: the eontimlitgoon'eetioo. thiogeare roneh hotter: wooin- put: Pt55158+=ﬁdeexsﬂ~5+ . 111-25”; Jr- 1251.3] — .2 =H—1meeeg: I'r enemies] = pm 5 z 5 meme] + Pm 5 z 5 esteem = tween + ﬂorets = [:LﬁﬂIl l3. Thin computed uaing the hill ﬂee-decimal plaoe mm; the erude aha-o'er le = pm 5 25 Leo] +1105 2 5 Mali = nestee+neleo1 = emaer. The picture minted with the. oaleldntioo Ming the oooti- nuit},I oot‘reetion le. shown in Figure 3- D.l'.|1. [I- l“: III.I.25 o.: DAT”. III-El“.- ELIE“.- [I 'i l:- T 3 FIGURE 3. The area hunter the normal etu'u'e [grayj with the oontdmlitg oomeetioh—ie, extending an extra 13.5 unlt to the left. and to the right—la a very good agnroximtjon totheareaofthe red hare. Note thetthe'rarianee H-211 no.3}: ﬂ.T-5.IZH in harer over the mle—ol—Lhunm value ofﬁ- whieh in reeomrheotletl hefore naing the normal apprmjmation to the binomial. El Problem 3 (15%]. The weight of "JD-pmd" Frog! qfeernen-t ore oe- amnod to he nomtnlhr Itr'otnitlutot. A amp-[e of“) huge ta mnltnrntg eheaen. wet it I21 found: that the rmemge might fie CHILD! prmnlte with o amounts alt-eminen- drool-mien ofa I112 men-iv. Fwtneitrgteﬁnd the 55% ermﬁrtmm minim-i for the two mom #- {a} Which ﬁre-Mitt!” dean-mm are you going to- uee: 2' or t? [h} M the Elﬁ'ﬁ. oonﬁdmee intendﬁw the true room it. SEEN-tit"?- {a} Une the tethtﬂhution. The key- wonh to- Lell you thle. are “enm- pie" atandard :ﬁatrilmtlon, and e = 11.2. {Lt'jlon were going to uae 3, Le. the normal, you‘d e‘meet to refer to "r!" and "atan— darn dEﬁMltIl'l"-} {h} We need the mitetf in“; for Q degreea eE‘ Ereeﬂem: Leaking it up in the Hem-e1 we ﬁnd ting-2h l 1535'}. Th: mnﬂrllmm intmrnl is givm lily — .1 I a: u— 30.1]: m l.e.I 13.2 EMMA: 2.113511 3-: 3.1% = inﬁll-1 1 0.169314. This could herep-erteﬂ eithermi EmmiﬂJi'. eras; [4935“.5ﬂ21]. El Problem -I {lﬁ'ﬁﬂh A “EH-n: I'll-It ." Hf Bimﬂnh Mhtnﬂy '||'|'|F!:IE-'l in .i'l-rirm mun-11.- ﬂuid new it mlm'nrr: the amaze-1m are nun-neith- dim Initiated with a mem ef 21113 ﬁnal-1 ﬂimr’i'l and a standard rteu'drinu njﬂﬂ ﬂuid dunes-J. {up Find the pmM-iem that r: mmﬁnﬂrdhdsm Mule 41:} Empuﬂnid weigh mere ﬂint: El ﬂuid aural-nu. [11f Find the HELP: jumble of the mini-mm e-f tutti-M afﬂur’pﬂﬂﬂlﬂ; a'.e._. ﬁnd the mine wl .m- EheJ! 9.5% nj' the Mule-i: ee-nlm'n m ﬂuid {mm or few. Sail-+501:— X— .1 {a} We have 3 = # 1e thermally dietrlhuted, am we are mitts-l I'm FLT 3 1‘1]- ‘I'IE ﬁnd Fur 2; 2]} = Fur — 90.13 :3- 1131'] x - 10.13 . p (—0.3 = PIE 2“: LEIIEI'i'Ej. Using FILE 2 LEE} RE the rmmrletl—eﬂ mine lﬁﬁllltﬁ i.11 FILE 2 1.09] = 0.5- - 0.36211 = 0.13m. Thin. mﬂl‘ul‘IH-ﬂﬂ te- twe deelJIml [Amen an. 0.1-1- 2 LEIE'i'E) [hp We need the mm. at gum = 1.5119 [uhtnh'red from “IE lent line of the t—thle at the had: at the heel-c: 1.645 in deﬁne eue-ughﬂl. 3mm My 30.09: e mm. m: were: want-ityﬂ {Eur “1.! “95th peremLIJe“,el1Jy E'E-ef the mainte the right: net 2.5%.: Tlu! ﬂEedI'Bﬂ 'ImhlE- in theme- 2113+ LEI-HQ :t llﬂ = 21.4459 ﬂuid winners. That in. PM“ 5 21.4.4591 - Fiji - 20.135 1.3159: = ﬁw 5 teams) I15 = ﬂ.9i'r. El Problem I. {1593'} A mtm‘n type a; ﬁght truth has e. um brightnem ej' TEE turn-um; but Wee turf-ex ﬂan-a. imtl'r ﬁe butt. and the etdndqmt dmridta'ma. it er = 51] inmates. .1 mun-after tluyw M3 in junta-um e)" E5; mane the brightneaaee are mew-dent met math utilitrihﬁtnt. {a} Wmmemeﬂnﬂndetundmmmtmnﬂﬂeavemge High-l- ine-m nfd We efﬂﬁ built-e? [hj III-Mi Hie mMHtﬂy the: the mange hnlghtnem raj" 2‘5 innit-e in HE tun-um er more? Set-I'm {at The avenge hriglmuem in. given by —_ XL+X2+"'+X1L H‘T (L11 Inmate—whatever them! are), Pu'u‘l minute the I; are IJ'IdIEI'I-HI- ﬂeet, Em] I H - TED humans. i_5ﬂ' aft—WE {If = = "J IIL'IIIIEIE'I- {h} We me theme ﬁgure» in [men |:l1-:I- We are eating fee Hie-T45] = PEI—mil a —e} T—T‘ﬂ] _ Ft 113 :_= 41;.) = me :_= 415} =%+F{ﬂ§25ﬂ.ﬁ} = 13.5 +ﬂ.lE|-1-lﬁ-2 I [Iﬁﬂlllﬂ-i. Se nhmut 39% Inf the magma 1II'J'II have an average hightnm elf 1'45 lumen-c DI' mere. El Prablemﬁﬂﬂﬁlj. EahyEemhieem-miymr,endyaﬂmmﬁeete ﬁlm il'JIe meme WW mrﬂme within in mg M ﬂue ESE. maﬁa-rm: Lewet All: 3m: new arm: EWBnum i5- me Me 9mm deviation ef the Minnie when: in ct - ll] Mia-rim. Hem mama mndy here .eﬁmld yea: amide eel whim-e the him-mes? Eel-mam. le‘re told the wane el rr: this mean". we‘re mlmllng yen knew the thm'lnrd deviation, uni: the wen-spite “tandem deﬂation. [An- other hlnL: we said "Maurine-ﬂ ﬂewintlen", net "mn‘tple Hmdmwl deut— ﬁtm".} The general Fennnln for 11 is IrhidI :irI- ehI-mn' erl ha- wiring zen” _ :I: VIE — :EE'. Here we Imve Renee: l-‘EIEE. r-r=1|L Inn-ﬂ E'=?'. thm the Hun-met i-i 1 I: = (w) = Hint Since :1 must he an integen we ehmllﬂ sample r: = 3'? emrly ham-i. El ...
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