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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 zscores that actually appear
in Table A. Round your fmam paces. Remember to express your answer as a proportion.)
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[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 WWIr) W/(BIOMMXMB 5' "’5 977565“ (5K wit774. {, 0mg 7 :: Z > lezreseé ' 2— D 033 0,2033
cps—0.7467” \ // (A;
>/ 3 The time X that a technician requires to ﬁx an airconditioning 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,, :: Ilaloo: Clo}
675,.” : (ﬁzz—+04, = (3)1460": 2r / 60”): 'U'zs" :@ 176V; Wt)
" 0” Z L > :{W/ :
/
66“) Warw) > 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>,XH) 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
earlyspeaking 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 earlyspeaking 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 earlyspeaking group (a? ) will be at least two points
lower than the mean score for the delayedspeaking 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+0 644“ 3: m 0,) K
M d If e» h +1 / if”? : 0.1:Ié131“'7/3 30.53
39 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 nonwhite or a voter who voted for candidate Jones? P(NW”L F) : ?(NW>+’?(F) rPvaw F) 1' OH + @Lntoo‘a)  0.08 Problem 9 (4.4) ‘5 ..‘.4—————v4.—— _ 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‘+ zéowJZOHJ/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. lef
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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 Fall '08
 ABDUS,S.

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