stat_exam2_review_solutions_fall11

stat_exam2_review_solutions_fall11 - adhifiz RQWEW Problem...

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Unformatted text preview: adhifiz RQWEW /\ Problem 1 F A SRS of 1000 adults asks if they agree with the statement “I support President Obama.” Suppose that 90% of all US adults would agree if asked this question so the population parameter: 0.9. Round the standard deviation of the sample proportion 13 to four decimal places. Using that rounded number, What is the probability that the survey result differs from the truth about the population by more than 2 percentage points? (Use z-scores that actually appear in Table A. Round your fmam paces. Remember to express your answer as a proportion.) (ram/w) ‘1': fl, 0044863 33 [moo “M03 Problem 2 A college decides to admit 13 10 students. .Past experience shows that 80% of the students - admitted will accept. Assuming that students make their decisions independently, the number who accept has the Bg 13 10,” 0.8) distribution. Round the standard deviation of the number X of students who accept to four decimal places. Using that rounded number, what is the probability that more than 1060 accept? (Use a z—score that actually appears in Table A. Round your final answer to four Etc—final places. Remember to express your answer as a proportion.) ' - W -.:’ (\smym :- /o'L+5* . p _ M649] - p X!» N Ear I . I WWI-r) W/(BIOMMXM-B 5' "’5 977565“ (5K wit-774. {, 0mg 7 :: Z > lezreseé ' 2— D 033 0,2033 cps—0.7467” \ // (A; >/ 3 The time X that a technician requires to fix an air-conditioning unit has a roughly normal distribution with p. = 1 hour and o = 1 hour. Your company operates 70 of these units. Problem 3 (m) a) What are the mean and standard deviation of the sample mean a? of these 70 units? Round your answers to four decimal places if necessary. ( / ' a flax—’- r XWM [my—5% W. a, m ., ‘Hasm’é b) What is the probability that that the average maintenance time 55 of these 70 units exceeds 55 minutes? Use your final answers from part a. Round your final answer to four decimal places. W v 99 Glogz) Problem 4 9 Y ~N (| 00) Tom and George are playing in the club golftournament. Their scores vary as they play the course repeatedly. Tom’s score X has the N(l lO, 3) distribution, and George’s score Y varies from round to round according to the N(100, 4) distribution. Their scores are independent. 21) What is the probability that Tom’s score will be at least two points higher than George’s score? Round your final answer to four decimal places. Méwj shy/4,, :: Ila-loo: Clo} 675,.” : (fizz—+04, = (3)1460": 2r / 60”): 'U'zs" :@ 176V; Wt) " 0” Z L > :{W/ : / 66-“) War-w) > 24o ' / / 6 5 (xx) \ _ 0.03% : Z —/léo Cp: 0.05% b) What is the probability that George’s score will be at least one point higher than Tom’s score? Round your final answer to four decimal places. ?(Y>,X-H) W N(l33,3°) 7 haloo 5 Problem 5 N61; 0) L; a) V hzmo Round all of your final answers to four decimal places if necessary. Researchers randomly assigned 100 beginning students of Russian to begin speaking practice immediately and another 100 to delay speaking for 4 weeks. At the end of the semester both groups took a standard test of comprehension of spoken Russian. Suppose that in the population of all beginning students, the test scores for early speaking vary according to the N(133, 30) distribution and scores for delayed speaking have the N(130, 40) distribution. Let us call the mean score for the 100 students in the early-speaking group a? . Let us call the mean score for the 100 students in the delayed—speaking group i. a) What is the probability that the mean score for the delayed—speaking group ()7 ) will be at least four points lower than the mean score for early-speaking group (a? )? >7~N(M,w§;> /7~M633,%§3 /)?¢N 033,3) \7~N(%7%) /37~N(uoj / WNW) M574) = A; “M157 2 t3?~l?o : [3—] 6L ‘ 5E + 61$ = (3)54th = 19 / 66H): 175: =51 (2'7) — M { #05773 : O,Ll’Zo7 S 6(9—9) 0120 S 2 Ce : 03743 b) What is the probability that the mean score for the early-speaking group (a? ) will be at least two points lower than the mean score for the delayed-speaking group (37 )? Problem 6 Suppose that the proportion of male voters who support candidate Wilson is 0.54 (gm = 0.54). Suppose that the proportion of female voters Who support candidate Wilson is 0.51 (pp = 0.51). A sample survey interviews SRSs of 40 male voters (from a population of 100,000) and 40 female voters (fiom a population of 100,000). The samples are independent. What is the probability that, in the survey, a higher proportion of male voters than female voters support candidate Wilson (rounded to four decimal places)? m? : fin: 0.9,» /({L : Wl—PM) ,: mmflm) 1+0 64-4“ 3: m 0,) K M d If e» h +1 / if”? :- 0.1:Ié131“'7/3 30.53 3-9 F /h:3 Problem 7 O "7 F : 0M7” The proportion of the American adult population that supports President Obama is p=0.58. A SRS of three adults asks if they agree with the statement “I support President Obama.” What is the probability that a majority of those surveyed would agree with that statement (rounded to four decimal places)? (Remember to express your answer as a proportion.) P (Kai) ( go,§3)1(0,‘+2)'] 4 (§)Fo.§?)3(0,¥2f] “3 Hf 0] 3 f a j 4 CL I ’7 .7 :: é / 8 a 7g Problem 8 A” 9" The voters in a large city are 60% White and 40% non—White. Candidate Jones Wins 70% of the white vote and 20% of the non—White vote. OWL \/ a) What is the conditional probability that a voter is White given that the voter voted for candidate Jones? 0 l LP 2 b) What is the probability that a voter is non-white or a voter who voted for candidate Jones? P(NW”L F) : ?(NW>+’?(F) rPvaw F) 1' OH + @Ln-too‘a) -- 0.08 Problem 9 (4.4) ‘5 ..‘.4—————v-4-.—— _ I“ . . _._.__—_.__.__ ____._..._.._.._._..___‘ .._- .__._.__ ____..‘._,___.__ Round all of your final answer to four decimal places if necessary. _ Consider the. following information about random variables, Xand. HX=5 MY=12 p=flA O‘X=4 GY=6 Consider another random variable: R = 0.9X+ 0.1Y. a) What is “R? flit? {big/1X +(0't)/u‘f’ t/o,4)(§\) f/O-‘362) 3': b)WhatiscR? [2: (0:4)X *(flDY : I: 4' 6. Z 2 62 t 6', ’I’ 66 A, : [0.4)1(632)+ [c.tb‘flé ) +7('0-“}[Dfl)/5¢Y0rD/5U :( 0.07% L01 +d/0J)7'/O‘+ zéo-wJZOHJ/L‘Mp'ow :— H.541 om ; mm H_—_.—_——‘_. . 1”. ’- 2HW70162 . 1 0 Problem 10 Round all of your final answers to four decimal places if necessary. The probability distribution of random variable X is given below: Value of X X= Probability __ A second random variable is defined as follows: Y = 2X— 1. A third random variable is defined as follows: Z = X2 — 2. Wham”? fix 1 1(0,Le)+4t(0.6) / b) What is 0321 ? 63 1 ('2.~3,2)2(0,u) a} (q -3,2)2(o,6) : c) What is 0'; ? d)Whatis0'§? :2. le-f OH Odo 2: (2)722 :. Z 2 = («352 -, 1L} M2 = 1(0'4) + “((0.6)‘2. 4‘1 'L ‘ r 6 %—. (24.2fm) +. (manifm) : ...
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