Sample Examination Four-Answers Section I I . (D) The maximum and minimum of Set X are 100 and 50, respectively, for a range of 50. The maximum and minimum of Set Y are 100 and 57, respectively. fbr a range of 43. Therefore. the range in Set X > the range in Set Y. For Set X. using the 1.5(lQR) rule, 50 is not an outiier. The interquartile range (lQR) is defined to be the 75th percentile minus the 25th percentile. In this case, the 75th percentile is approximately 90, and the 25th percentile is approximately 67, for an interquartile range of 90 -67 =23. Multiplying 1.5(23)=34.5. If this value is subtracted from the 25th percentile (67);the lower bound of 32.5 is obtained. Since 50 is higher than this boundary value, 50 is not an outlier. The amount of data in the two sets cannot be determined from a boxplot. The interquartile range of Set Y is visually larger than than the interquartile range of Set X. The 5-number summarv in a boxplot includes the minimum, quartile 1. median, quartile 3, and maximum. 2.(B) Since x= 2 and )'= 1'1. g'e hare 11=2.2t+ I l0 = 2nt 5--nt Therefore, the equation of the regression line is )= 5x+ 4 and y= 5x+ 4 3. (C) Since the mean(7o/o) is much lower than the median (12%), this implies that the distribution is sker.ved left. The mean is affected by extreme values. 4.(B) Using the formula ,=+ left-hand area of 100% - and the critical value 0.675 (which corresponds to a 25o/o = 15%) 6-t5=r+L 41.25=475-p 42j.15= 1t = 4Zg ,, t. o=70 46 or reusrng any part of this page is illegal. 475 'tPDallr sr a6ed s!ql 0ursnoJ Jo 0utIdoJ lo UEd ^uE arllrg o1 Sutp'toccv'%gT.,{leleutxo.rdde ro Suruur,n Jo ecueqJ Jelleq € suq eqr os [(e 's) .orueiJ lsJU aqi ,s:eqrun51 'e3;e1 seuocoq ,/ se a8:e.1Jo ,\\€.I aql ff sr lq8re ro xlsJo r.uns e 8uri1or3o ,Qrilqeqord (s'r)(z'g)(g'z)(r'r) ,o (s'r)(r's)(z'v)(v'z)(r'e )] sre,r 61 ur ueddeq uec lq8re ro xrsJo r.uns e 3ur11o.r'pueq reqlo eq] uo 'o7o2y Klawwxo;dde ro f; sr uenes Jo runs e 3ur11o:Jo {rlllqeqord aql [(t'r) (v't)(Z'E)(s'z)(r'q)(q,t)]s,{e,n 9 ur ueddeq uuc uenesJo uns e 8urylo.r ocurs 'uorlplndod oqtJo rf ueeu or{i seqJuordde f11en1ue,ne senl€A pe^Josqo eqlJo x u€eu eq] 'sesuercul u^\eJp suorle^rosqoJo Joqrunu aqt sv (v) 'II 'senlel patcedxe pue pe^lesqo eql uee,{\}aq ecuoroJJrp luecgru8rs ,{11ecr1sr1e1s e }ou s€,r ereqt }eq} sel€crpur Ilstus sr ,x so enlen eql ]eql }c€J oqJ 'srseqlod,(q IInu oqt lcafe: o1 a3uaprno qSnoua lou sr ereq] ]er{} o}ecrpur sen1e,r.-d aErel 'e3"re1 sr en1e,t-d aq} 'lyeus sr ..X ecurg (61) '01 'alqrssod s€ Il€us se eurl uotsso;8er oql pue slutod elep oql uoa,ttleq socu€]srp Iscrual eqlJo sarenbs eqlJo rulls eql so)Bru l€ql eurl eq] sr r( uo ,{go ourl uorsseJ8e: se:enbs-}s€el eq] ,uortrugep {g (C) '6 ']coroc osle st JI e.toJalaLI] 'uerparu ueetu eql os '(1re1 eql s,4\olloJ ssaumels) UOI peMeIS sr rrortnqulslp eqJ .lcorroc st > III os '(%0S 'reddn oq] ruo{ Zo0S ra^\ol aql saleredes 1r) enye,r uetpaiu aqt sr sree,{ I (g) d 'enle^ or.ues eq] seq uorle^lesqo qJes l€L{l seiecrpur oJozJo uorlur^ap pJ€pu?ls u 'ueoru eql inoqs peerds oq] seJnseeu uorl€r \op pJepupls ecurS (g) L 'pasJs^ol eJ€ So[QsrJBA ueq,u e8ueqc lou seop uou€larjo:) 'pe8ueqc ere sJlqpue,\ aq] Jo sluaruarnseoru Jo s}tun eq] Lrorl,r\ eSueqc lou seop -r'suorlen;asqoJo sanle,\ peztplupu€ls sesn l e3urs 'alqrsuodser eq ,(er.u elqeri€,\ 8ur1:ny y .drqsuorlela: lJeJJo-pu€-esnec e eelueren8 lou seop solqerJe^ o^\l ueaA\laq uorl"laJ:oc Buo:1g 'olqsuorl€leJ Jeeurl I€a,\\ e 3l€crpur 0 Jsau /Jo sanlen 'uorleleJJoc eq] lJaJJe uec slerllno 'uorlernep plepu€is pus uearu eII.1 (A) 9 '('raleruered) uorlelndod aql ur lserelurlo uorgodord aqtgo anl€^ or{} lcrpe.id o1 (scr1sr1e1s) sllnseJ eldrues sosn lenrelur oJuopguoc y 'pe{a,uns ueuryse{ go luec.red eql 7da pue esrnoc qletu e elel 01 Suruueld a8eluecrad eq] ol sel€leJ roila Jo ui8;eu oLIJ (g) LN sJa,llsuv-Jnod uoUBurruExg aldurug I I u0rlJas Sample Examination Four-Answers 48 Section 12. (B) This scenario has a binomial distribution. success, then P(success) =9.15 The formula for the binomial is: P(X= k) = (,C)p*(l - p)' where - I If we call an underweight package a o ,C*=;/L " ft!(n - ft)l So, P (3) = ( sCr) 0. I 5r (0.8s )' = i t o ) (0.003375) (o.t zzs) = 0.02438437 5 P(4) = (,c,)0.1s' (0.85)'= 1s;10.0005062s)(0.8s) = 0.0021 srs62s " P ( s) = (,c,) o. 1 5' (0.85) = ( t) (o.oo 007 s%7 s)( I ) = o.oooo7 se37 s P (x' 2) =P (:) + e (+) + e (s) = o.oz00 Using the TI-83: I 13. (c), =- - ! sl - [Binomcdf (s,0.15.2 )] =0'0266 3:- = 3.?j --l1.53r Jn ,'25 = 7:7 ftr:8 sr: L53 5 Using the /-table with 25 - l = 24 degrees of freedom, we see that 0.001 < p < 0'0025 t4. (E) If the subjects do not know which pill they are taking, the experiment is singleblinded. If neither the subject nor the experimenter knows which pill is being taken, the experiment is double-blinded. 15. (E) A is a normal or rounded distribution. B is a rectangular distribution. C is a left-skewed distribution (skewness follows the tail)' D is a histogram with no set pattern. 16. (B) With stratified sampling the population is subdivided into at least two different subpopulations. A random sample is then drawn from each sub-population. 17. (c) Expected value is: or any part of this Page is #Hitr r=W=rru 'lE6all! sl e6ed str0 lo Ued 6ulsnel :o 6ulAdoc pezpoqlneu ^uP %6E t ,(leluurxordde ro t8tg0'0 =(V'02'08'LZ) (uorlernep prepuels 'ueeru 'punoq raddn 'punoq re,troy) ur ed,& pue reluo ssa.rdgpcleu.roN:Z sren puz :rolelnclpc €g-lJ eql asn uo %6;L - 8t66'0 :eare;a8re1 ruor; eaJe rell?rus tcerlqns 6696.0 sl Sl.t = z qlul\ ,Z 1y\oleq uerv 9t66.0 sl g.Z = z qlrA\ 0t ,^^oleq eerv 'elqel uorlnqlrlslp I€rurou eql uo ee.le Eurpuodse.uoc eql dn {oo.I sr qcrq,\\ 6€€0'0 = 6696'0 @ -*) g.7 = ----F(02 gL'r = -4- 6z- tz) = z uolJ€hbe - 0€) - z sr erocs-z eql z Sr oJocS- z 0t punoq raddn aql Joc erlr LZ punoq Je,rol eql roc eql olul olnlllsqns 'enleA qcea JoJ eJocs-z eql pulC %6E t (C) 'rz :t8-ll t0l pu? 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(A) 0.0038 Find the z-score by substituting into 24) the equatio n r=Q--lt) , -(BLook up on the normal distribution rabre the u..u .o..ffi,nrXo= The area =0.003g or 0.3ga/o OR on the TI-83 calculator: 2nd vars 2: Normalcdf hit enter type and in (lower bound, upper bound, mean, standard deviation) g.24,6)= (_ 1000, 0.003g30 or 0.3g% $*=-'uuu 23. (D) 9.55 The standard deviation is the square root of the variance. Variance=16,o=fi6=4 The 35th percentile corresponds to 0.35 which is the area under the normal cun,e. Looking up the area of 0.35 'nve find p) z=-0.39. Substitute in the z_formura ' \vL\"ut. {,_(r- -z(s therefore -0.39 -p) Multiplying both sides by,. 4, rve get + (- 0.30) = S _ 1t thensolve for p. F = 9.56 OR Use the TI-83 calculator to find the.z-score 2nd vars 3: Invnorm hit enter and type in (left-hand area. mean. srandard deviation) (0.:S.0, l)=_ 0.3g53 which is the z_score. Substitute z-score in a[rore equatior and the answer is 9.54r3 24 (D) 149. The degrees of freedom are /r - r rvhere n is the sampre size. (1501)= 149 25 (D) 1'746' use the table of l-distribution critical values, with degrees of freedom (df) n - | = 17 - | = 16 and confidence level 90oh, t = 1.746 26' (D) A normal curve is always symmetrical and is never skewed. It only has a mean of zero and a standard deviation of one rvhen it is a,stanclardnormal curve. 27. B)3/l\'/!\' \o/ \6/ Using the binomial theorem ,,Cr(p)o (r1t'' ') ,"h"." ru : number of trials, p : probability of success, q (l p): probability = of failur e, k : number of successes, ..,. ,,,31 , /l)'19\'=./ t\'/st' k!(n-k)t ll(3_ r;r\6/ |r6-l =r\a/ tai nCr=;,,'1 uthorized c opy n 9 oiie uEi n gany part of this page is illegal. i I 'lP6oll! sl abEd slql lo UBd ^uE ro 6ur^do9 eu t9ol9'o = 16,^ \ 'os'vs'8v lit )JPrle..,roN '(ezrs eldures Jo looJ erenbs4rotl€rnep pJepuels 'u€etu 'punoq ;eddn 'punoq ra,no1) ur ad.{1 pue ro}uo }n{JpcleuroN:Z sr€^ puz:ro}elnolsc 9019'0 = EFLZ'0 - 6t88'0 ea'te ra8rel tuo{ €e.re t8-lJ aql esn uo rell?us }certqns ts Molaq 80rv 6t88'0 sl Z'T = z rllr,^\ wLZ'0 sl 9'0 -= 2 LIlr,\\ gt ,t\oieq Berv "alqu] uorlnqlrlsip leLruou eq] uo eere Surpuodsa::oc eql dn 1oo1 {{\ / e , - -WI "', 0g:k I o/\ 9'0 YL (n 0 -r) - z sI orocs-z aql tS punoq raddn oql roC \ff/ -= Oi;{7 - z sI orocs-z x[ 8f punoq ro.t\ol eq] roC - ? uorl€nbe eql olut olnlllsqns 'rills^ uces ioJ eJoJs-z oql pulc r r9'0 (o 'zi 'enJl eJe sluel'Uo]€ls IIe sJueH 'e^rlrsoo qloq ore tdec.retur-x oqt pu€ ldecrelur-,{ eq} lnq uol}ularroo a,r.tle8au e seq (3) ern}ctd 'o;ez edols r{}ln\ ourl l€}uozlrotl ,{lelerurxo.rdde ue seq (g) ernlcrg 'oroz r€au "/Jo enl€^ e sarldrur (y) e:n1cr4 (g) 'tg 'uotl€sn€c 1ou 'uorlercoss€ JeaurI SMoLIS LrorieleJJoJ 0sn€caq osleJ 'paleler sr ill Xlasolc are selgurrp^ aql Jo ,{ueut ,rtoq et€cIpur }ou soop }nq uor}€lerroc rueurl e,trysod oleJoporu o1 8uorls e sluese:deJ gL'1=t'as1ug st 11 'en:1 sl I (V)'0t =, (oos.o) 'lapow uorssa;8e'r eqt ,{q peureldxa sr t€qi euoqdelal oql uo lueds srnoq Jo J3qunu eql ur uor]euul eql Jo e8eluac;ad aql sI poJenbs "t (3) '67 o/o9 L '67'9 uegl ;e3;e1 eg lsntrl runtururru SILII '6Z g = f , ,9;O _[(st0'0)\sveI))'l ,g ,E€0.0 g ,SVg.l - z Z0'0 = JoJJa Jo ur8;eu eql f ,+ " -l(ol*2 7.', IS sJa,.rl.su11-Jnod l= 11 Sr oZrS aldues roJ €lnuroJ oLIr .6 (J) .gz ) uorluurrusxf, aldurug I uorlros Sample Examination Four-Answers 52 Section I 33. (A\ 2 The standard error ir -F. v'll Since the standard deviation equals the square root of the variance, o = /tOO or 10. Substituting into the standard error formula we get: l9=r Jzs 34. (C) (0.2177,0.4489) Substitute into the formuia p + ^ P= 7 15 A< The z-score for a 90oh interval is 1.645 't< /l 15 tr3u /\Jli\+-.\r r '^",= i+tt.645,! 4) | +) 0.3333 + 0.1 156 = ( u l 171.0.4459) OR Use the TI-83 calculator: STAT tests A: 1-Prop Z-intewal. Hit enter and type in -- 1S n=45 C-level: 0.90 arrow dorvn to calculate. hit enter. rne get (,0.2177,0.4489) copylng or reusing any part of this page is illegal, 'teoailt sl aBEd slql lo Ued IUB 6ulsnar ro uorlnqrrlsrp ftrilqeqo:d srr{}Jo luns eqJ'ouo eq ol seq sel}lllqeqold eqtSo '9't sl luns eql (O 'OU 'Jorre ll ueqa srseqtod,(q IInu aql Eutlcefe.r sI Jorle 1 ed'(1V '0S aql sr esl€J sr lr ueq.^ srseqtod,(q IInu eql iceiar o1 Eutltzg (C) 11 od,fi e Jo uoruugop onJ] sr sr n 'sseccns go ,{lrlrqeqord st a (l' tS0'0 le8 ot (S'Z'0'ZI)JPduoulg lunoc lc€xe oqi slry pu€ sleulJo raqunu el{l d'u) lVdtuourg :V srel puz rol€lncl€c €8-lJ eqi esn , \ , -,i(s-zr)is t^.^\ /-.. uo ts0'0 =,(s'o),(z'o)"-A-- =r\8 u/s\c 0)zJs .(o\ (d)rl' ?lnruroC lBIIuouIg eql olul elnllsqns (r u)t 'slueure]€ts ]cerroc ')' s0'0 (s) 'ac er' III pue I q]oq'eroJoroqJ'0e'0 sl qclq^\ (x)a ueql ralear8 eq louuec uollcasJelui JleqlJo enlel oql'S0'0lseol le eq lsntu uollcosJelul (B) .LE rreql Jo onle^ oql '1 u€r{} re}eer8 sI qclq^A g0'I =(,f)a*(X)a ocurs III pue I =(t -Z)n slunor ]cexoI -l osn }sntu em s1.rr3 7, $Dal /, ul po}seJe}ul eJe e^^ esnsceg SZIg'0=[(t'S'O'S)Jpcruoulg- I]1eB e16't puu I ruo{J JO^^Sue Jno lceJlqns 'lunoc icexa eql sI r/ pu€ sl€IrlJo requnu eq] eql esn sr zr,sseccnsSo,{Ilrqeqord sr d(l'a'u)Jpcluoul8:Vsr?^ puz rolelnrl€c t8-IJ uo o)- r ((o)"I+ (I)a) - r = (s1-rr8 z tseel 13 Jo)d (s'o)u(s'o)i(o -J)io - (sura ou Eur'teq;o)4 9zr8 o =(sztgo'o + szggr , \, (s'o)u?A= .i(l-gt" SZgsI'g =u (s'o), g'6 sr ;o ,{irlrqeqord : (a- f )-b '(' -,u)itl - )r, iu 'sseccns 3o ,{1111qeqord (b\ 1.uB e (urE auo 8ur'req3o)4 8ut,teq3o ,{lrlrqeqord eq1 'sassaJcns Jo : d's1etr1Jo : ry 'ernrreJ requnu : t/ erel{ltr requnu (d ) r3, elnru-roC l€nuoulg aql olul elntllsqns 1-1"4' szts'o(g) '0 }? u?ls o1peeu lou seop slxe leluozlroi{ eq}Jo elecs 3qJ 'srxe-,( eql uo sr fcuanbe4 aq1 .(s.rer1]no Japrsuoc ,.3.e) sreq aql uaoA\leq sdeS aneq uec stuer3o1st11 'sselc qcge3.o,{cuenbe4 at{lol pot€ler er€ sreq sqlJo stq8raq eqJ es sJonasu1r-Jnod uollsuIluuxf aldruuS (f,) ,98 'S€ I uoflras Sample Examination Four-Answers 54 Section Section II II Question One p= pt, of boys who admit to cheating pz=proportion of girls rvho admit to cheating Assumptions: Population is at least l0 times the sample Ho'" t1^'.p'> nfu p' pr =proportion Forp:550(0.434)=2gg >10 For n(l -p)>10 p2 :430(0.434) = ffi = 0.46 g.4 'pr= ffi +Jt.r = e= 1gZ a=ffiffi=0.434 Forpr:550(0.566)=3tt For pz:430(0.566) = 2qZ Note: In problems that deal with proportions, some texts use np and n (l - n) > to rvhen checking assumptions, while othertexts use the r,,alue of 5. please be advised that as long as the student shorvs that the assumptions have been checked, either value is acceptable. 0.46 - 0.4 0431(osoo)(#-r*) = 1.88 TI-83: 2-proportion ;-test, r= 1.88. p = Lr.03 All assumption check. Also assume SRS. z: 1.88 Conclusion: A z-score of 1.88 results in ap-value of 0.03. Due to the smallp-value, to be enough er.,idence ar d, = 0. 0 5 to rej ect Ho and state that boys are more Iikely to admit to cheating than girls. the re appears {)uestion Two (a) Assumptions: The data are an SRS from the population of interest. The popuiation is at least I 0 times larger than the sample (Rule of Thumb I i/ is so ). large that both the count of successes np and the count of faiiures ,(l-it)are 10 or more (Rule of Thumb 2). (b) The first assumption appears to have been violated, since using a random sample of high school male students omits the female students and those students under high school age. The second assumption appears valid as we assume thatthere are at least l0 X 750 = 7500 students in the public schools of the ma,ior US city. The 3rd assumption appears valid as 82 successes and 668 failures are both l0 or more. Note: students may choose to use 5 in place of 10. 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'leOalt! s! aOEd s!ql 6u1snal ro 6u1,{doc lo uEd Iue 'puriq-elqnop eq plno,ry\ lueurredxa eql ueqJ 'Sutntece: etu slcafqns oql euo qclq^\,arroul iou soop osJ€ luaurrredxe eql Suuolruou pue 3ut:elstuttup€ Jol{cJeeseJ oq} pue oqeceld oq} Jo luetuleeJ] eq1Sur,tracoJ oJu feqt reqleq,r\ A\ouI iou op slreiqns eql su 3uo1 se'sea (c) g dnoJc cI Ig eredur a)-" \ uatuold vdnorg sJeelunloA g dnorg g141g eredru o3/ \ v dnotg -/ u"^ utqll{\ s}lnseJ eq} e"iedruo3 'g dno;g :o y dno.rg olut re pue8 Llceo JO sroqlueu u8tsse ,{luropue; ueqJ '}srg uouo,{\ pu€ ueru a1e;edas'ssoi CNBJo sloneJ lueJaJJIp eruetrodxa ueulo,lr,r pue uetu oculs 'dno:8 lorluor aql se g dnorS pue dnorS uol]€clperu ./rr3u s€ y dno.r8 ,{Jltuapl (q) '.repue8 qc€e 'pue eql le sdnor8 o^\1 eqlJo sqnsoJ ereduro3'osn ui f1]uer:nc lueuelddns '}ueulelddns eqt eAIosoJ plnom 3o aci,{i req}oue alrecoJ plno^\ dno;8 loJ}uoc eqJ dnor8 lueLuleeJl aql 'dno.r8 luetuleoJl e pue dno:8 loJluoc u 'sdnorfl luoJo-illp oA\1 oi sJoolunlo.r. uBtsse ,{ltuopue-r a1qu11i3rp uopuuJ e Se qcns poq}aru luemu8tsse ruopusJ Jeqlo otuos esn JO leq e olul sJeelunlo^ eqlJo setueu eLIl.{\oJqJ (8) 'iuelqo:d u8rsep lelueutredxa u€ sI snlJ rnod uopson} 's|1 ,,arues e{} ,{11ertuessa.. aqt elrdsep peIIn3Jo aABLI iqFILu seJocs ur ,{luedsrp A{oQ uteldxa pinol\ qJILl,\\ pelelerun eJs lsa} sipls FurpesJ slq} uo eloJs pue Ol teqt elqrssod sr i1 'sdno.rfi o\u ot{1Jo s}l a8era,te eql lnoqu slue1lle}els eleu oA\.Ir sllnsar;no SutztleJeuaS-te.\o al€ a\\'soJoJs isat Eurpea: aJa.tr ulep aql oouls (c) 'uorl€r,\)p pJ€puels uorlelndod laqire uerlt ssel st se3uoJo$tpJo uolinqr.ilsrp Surldr,ues aqlJo uotlei^ep pJ€puels aL{J r( t'n =9Qll =- qq.i * AQi/ = oql t ''u- _cL -!L_ 9l | - r,8,vA$/I =9+lLi'='"-'"p Lo*-Pl (q) '0t -'t-'tT/ suorlelndod o.,rrl eql roJ sueeu oqt Jo eruere,+Jlp eql slenbe sdno.r8 oml eql 3o se8erene eql uee.{\iaq secuoreJJlp eq}Jo uolinqlrlslp Surldrues oqlJo uualu eql (e) uaroeqJ ittul'i IeJlueJ sqlJo esn sanlo,\ut uotlsanb stql aarql uorlsan$ sraiilsuv-Jnod uolluurruuxg aldruug II uollras 56 Sample Examination Four-Answers Section II Question Five This is a one-proportion z-test. Assume 40 kicks constitute an SRS of all kicks from that ranse. Assumptions: npo>10 and n (t -p,) >10 40(0.+s)= 13 40(0.ss\=22 So conditions are OK. problems that deal with proportions, some texts use nro and l0 "(I -f,)> rvherr checking assumptions, while other texts use the value of 5. Please be advised that as long as the student shorvs that the assumptions have been checked, either value is Note: ii-r acceptable. i:io: P = 0.2i5 LJa: p > 0.45 1t D=?-;=U.tt -+u where p : tire population p-vaiue = 0.028 0.028 <ri.05 o= proportion of successfui field goals from that range 0.0-5 level Conclusion: The lor', p-raiue slrosests that rre can reiect F{o. The data suggests that Stiiafi's summer n'ork made an improrenrenr in his field soal kicking sllccess. oR. Use {ire Ti-83: 2nd vars 5: I-{it enter and type in po= 0.45 x=24 n'= 4A Pro;;>P o = .9t)l p-v:riue = 0.02E z I 1 Linaulhorize.i uopying oi reusing L_- 1lJ !,1I or.i',' !_!1s_-elx 1gg" | _l I 1 Prop-Z-test 'tPOall! si o0?d slql jo UPd ^uP 6ursne: ro 6u1,{doc 'q8rq oo] eq ,{eur orn8g 'ulrBio yo\E eqJ' s.333llo3 eql alndslp ol ecuopl^e qSnoue eq o] sreedde e:eq1 t'H ]c far e,\\ leql solldurl en1u,r-dllerus eqJ Ltg0' - d'89'Z--z Aaa _ v u>c-^ 096 =u 'ezrs aldues eql sautli 0l aq ptno,t\ qclq,\\ ueurqso{ 9996 ueHl eJOIu ere orot{l }eq} eunss€ oslv '01Jo eceld ut g esn ol osootlc,{eru sluepn}s :eloN 'XO eJs suotldunssy ZL9=(t'0)096 '882 = (€'0) 096 '01 < ( "d- t ) u'01 <"du3o qcee ]Eqt pue eldrues trlopuuJ aldrurs e uo4i st eldrues Jno leq} eulnsse ot paou o^& €'0 > r/ :nH ss€[c uP{.uqse{ atil ut sluapnts IOouJS q3tq ale,rtrd jo uorgodord aqt sr de'reri,q g'g =d :og lsel-: uoluodord- 1 :tB-l.L (c) St.0 = ( g,e tt'0t )1poLuoutQ- I = (t ;.r')a- t = (p 1sea1 le) 6 (q) '%0t 3q lsntu luapnls Iooqcs elenud e 3ui1ce1es.;o '{lipquqo:d aqt'poq}eru aq}Jo sselp.reEa: leq} sl(a1 eq1 'sllnsaJ luere31lp i(1lq3r1s p1ar,,t i(eur pue alqeldaccu ere sluaruu8tss€ Jeqlo :elof{ o/o{.2 0 0 0 OI 6 8 o] 6 - L z 0 v 9 s v 8 II 7 t = €.7.. o =T = (o < ") a I lunoS 0 g1 go dno;E ur sluepnls Iooqcs o]€AIJO Jo a :uorlnql4srp 8ul,lro11o1 eql ansq eA\ 'sluepnls looqJs crlqnd luasa.tda.t E pu€ sluepnls looqcs ele,tud lueserdsr ol Z pue I '0 sllSlp aqt Sursn (e) xrg uollsan| /c sral{suV-J nod uollurrrrrrExE aldruug II uorlros
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