421-summer-08-e1-sol

# 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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