421-summer-08-e1-sol - STT 421 Summer 2008 Exam #1...

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Unformatted text preview: STT 421 Summer 2008 Exam #1 Instructor: Erkan Name Name: \AS—kruc 359 r ‘ S SE lUll’lfiarL S PID: .W Instructions Read each problem carefully. Show all your work. Credit will only be awardedif your work is included. Problem 1. The following relative fiequency histogram has been con— structed 0n the basis of 100 entries. (5pts)a. Find the missing height over (10,15) and restore the frequencey table for it (make sure that the total number of entries in your ferquency table is 100). (Byte-,2, HA1. SW pg. +he. reiaH-Je. gmcxmmcfieS I25 A—g _ "HA—e WAS-93¢“ gfefimgx.‘ , ., 0.2 . i ’3 (5pts)b. Does the form of the histogram How to compare the median and the mean? Which one is greater? Explain the criterion. Veg : M-ecbim > Mean [me cm 45 ?M\\£-& ’i" W ‘___..q arqu 215 Cl slaw {CH/u: Q2 4r Aiéerflouénm. (5pts)c. What pmportion of the observations fall above 5? 4,, [0.4) ‘2': CL“ ‘0! _..__——-- 024+) Problem 2. Given the data set % , 6,11 13, 1:, Mill, 2/ (aa/ziw (5pts)a.Make a stemplot of this data. ex Md: s—lemflo‘l' o “$23921; 0‘ [email protected]@%% Ll“ o 65.86 0 5 68' 1 13M? 4 -0 [email protected]' '\ 735— 1 ’1 g (5pts)b. Calculate Q1,M, Q3( first and third quartiles and median). M 2: 5' a ,1 .1‘.‘ Q. (5pts)c. Calculate the interquartile range (IQR) and point out outliers, if any (use the 1.5 x I QR criterion). Make a Boxplot of the data. “QR: lgafigz’fl J Q3+Q5319K=13 + Q5)“ @13— 6.531193R': 2- (3536‘{ Wail-— (glow) Pfgblem 3. For the following small data set '5 $1 = —2, 332 =4, 1173 =1 1 Calculate the mean at and standard deviation 3;. Hz: “will 1 : (taerQF‘) ) , 5 ,2’4— 6 __\ _(Q.2\) $19 rfi~ ’— 02 27> 3 W Problem 4. If the standard normal density curve is drawn, (5pts)a. What is the area. over —1.8 < Z < 3.1? i:i:2::::ZZt:F zmqqfi-«-CKBSSQ::61QGHJ n 34 [8‘ (5pts)b What is the value a such that the area over "a < Z < a is 0.92? m- "‘Z‘°”=O'% ‘ a: e - Gk _ Problem 5. X is a normal random variable with ,u. m 6 and a = 2. -(7.5pts)a. What is the proportion of values that correpond to X < 3.5? F( X (3-5): P( X35 < :f(£<‘1.§$€] :W (7.5pts)b. What is the value a such that the proportion of X > a is 0.35? -- ' '):1Q65 Q’é.~aofi. . fl PQX<Q é, ’1 W a i an“ fl 2 <Okfjgaes %$6+@,7 Problem 6. The heart rate of a certain population is normally distributed with mean 73 beats per minute and a standard deviation 9. (7.5pts)a. What proportion of the population will have heart rate within 55 ands” F<5§< x 482 33' P(ss‘—13<—Z < 822173) “I m :—- vl<z< 4): cglfla... 5‘9128/ 55 13 32 ‘ (7.5pts)b. A person falling in the top 10% is considerd “high risk”. Find the “cut ofi" point beyond which a person will be considered to be in the “high risk” category. ‘ F( X (Cl): 0.9“) E I Rafi: 3 33M 4 t 0‘ ) a U 314,52 (“jig :tfifi sue—sf Ci: Ssh-S pmmaméymm the scat-terpiot of fecfii-ns'fmmZS- Fidefifir “sector funds” '_'.'i112902ané_1in_2{}83. " ' "' ' " ' " 5311.56 tile ébm :eq . . . . . acid: {dads in 29.62 for valfiéj ' 3 gain year; 2653. "‘-:‘-m--‘ atign' '1? flag. {mast SQ gaging to am; me ' mag '95 Z _ _ a: 5— E” 2 Q-«(oa’LC—I) 2 2. Problemg (4pts)a.(_)alculate the correlation for the data. below and decide Whether the linear model can be applied for the data. (To save you time I give you the values 5'5 = —1, 556 = 1.826, 3'} = 2, 33, = 1.414). ml; Z (2min ‘—-" "' ‘6‘ 3’ n “(n-Ufaxgj - U i Y ('93- l __,__L_° M ‘ . _ ._ 24,...___7__— " 3 Uglguhm?‘ RES-M 3M +( Ilka-1) +b + (lltll) 3_U.ggl.:)u.mq :2 {9.615) TM (2’: 0\ Wink S35w% aapgfihw mesomahon béjrween 7&0“qu é (5pts)b. Make a scatterplot of the ab0ve bivariate data. Find a and b, and fit a straight line 1} = a + ban to the above four bivariate data points. Plot the fitted line on the scatterplot. EDT—$5 =(o‘eouLClflfll: 9:1 5"“ ' (L326) 3?: 2.": +1331 24 W____._. (2pts)c. What is your predicted value of y for 2: = 1 in part b.? What is the residual at the point (1, 4)? le é J. (gawk 0.1» (Ml—0’:— 3.if : a; (1pts)d. If we want to predict a y'value for a: = 10, what kind of a prediction isthis? - extragLOKqun Since 10 {,‘S “J” l“ W WM [#3: A] ~ % I a randéiniy Prcblem 9. 10% 9f undergmduates and 20% of graduate students: in a ' ' _ _ ' certain3831iversi£yzgr§foreign students- 75% Gf-all' the students-axe'gmder; - 3-%Wiuatesand-25%;aregmduafiasa _ .i . ' . .- v .: _ as: (CPR-3 _' I :Find'th'e pmhahiiity mafia- Irafiéqmiy chosen. sfiud'ent is foreigfig jUSijIhie- - " - - --£r.es‘3' déagmm'a-i-i-I-ii " " ' - '- ' '- ' .3.3;32¢.fi_lg..o- f-fiwet ':’§Q{‘¢_€§<\ ' : ‘ .-:-'u_i}dergra(igatei [email protected]: he orashe iis a fare-ign Swami ' ' ' ' ' . -.Probiem_ 10, items mining :off a production fine are. categorized asgood- -_ ' . 2(6) and defectivé'(-E); aficiflthe yemientagas are 95% fer good and 5% for . . _ ' defective. “Suppose thatfrggqitgnzs wiiirbeiseietted.ramiomiyifcjf'impeéticin .- -' ' 'i'and} theséiecfibnsgate:ifidépémient; (Hint; Lei: 61,92 be the first am} sémnd : ' 7 ' - _ ' _' item Selectedto Begécii;frepectifieiyysimilafly define Di, I); for d‘e'rfefitive; - " ; " , - _ w '_ .ifieans. Show. ti'xeievents;insqaeaifiionion a Venn-diagram). _ ' '3 - -. I . (gr3.5)a.__Find_th'e_ 'probabifiiy' £113.13: Zat._ least? (me of the items is defective. '- P1363 4-w- £93513.?k¥>r:+éib:e§¢?5f * a I i " ; 1:1; E557137";- ' {was} an} Féné'fiiéprobébifitym gagigarggiggggmg: gage}; . -- ' -_ ,1: -- c __ - PM)" av.- Mz')‘; P'Cézi>3K§.13.}.5”£.--...i'i-E} " i113 *- 7 r ' (WM-#41“'fimméf fiiiaiti‘éiiiéi 101*- théiéeif .. .. _ _ ...-.i<éiéiitit'<{=ms 13.3003, miss iae: .-pmbabiigtygihgt;both citizen: gig-ggafit§_gzg_ - - r .. 1 jff;;_§ijsg.;j_§] I ' =ng'7i_1:¢és§”fsgg¢* 59?; “.35 Lfésg'é'effj“?ifffsfggijE .; ' m; " 2 m 0‘3 9 9 6r"- 3: ...
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This note was uploaded on 07/25/2008 for the course STT 421 taught by Professor Nane during the Summer '08 term at Michigan State University.

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421-summer-08-e1-sol - STT 421 Summer 2008 Exam #1...

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