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solutions_to_second_midterm[1]

# solutions_to_second_midterm[1] - Math 124.13 Spring 2011...

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Unformatted text preview: Math 124.13 Spring 2011 Helen Finkelstein Midterm #2 - April 7 1. Here are the responses of 178 students to a survey. The question was, _“Do you think 8 am classes should be eliminated?” The responses are shown separately for the men and the women. opinion yes no totals 88X a. How many of the students were female? ‘38 b. Find the conditional distribution of the numbers who said yes given their sex. Molt; L3,; 3 .5") =§7qa l- ‘_ p: l Eggn75~7sﬂ c. Describe the association between opinion and sex. _ Fe NM (new 0L [(212512 mm W +0 3&7 M 9m cuss.“ SW at £102qu- 2. In the game of Craps, the chance that a player wins on the ﬁrst roll is about 22%. a. Find the odds that a player will win on the ﬁrst roll. (“‘21: 078 odds: '27-‘4. .1? ”A .TX‘ ’ b. Find the chance that a player will not win on the ﬁrst roll. l A. 2.2. =71? a "13°70 3. Betty is gambling, playing a game called Ulose. The chance she will win the game is 10%. If she wins she will gain \$7. If she loses, she will lose \$3 (for a gain of -\$3). The different games she will play are independent. a. Find the mean (expected value) of Betty's gain. #:1610) +(_33(.qo) = .’1-—’2..7=- b. Find the standard deviation of Betty’s gain. = (1 «(arm ‘+ (-B—C-z>l"(-90) = ./ Wm ant—0‘0") “ah-rm = [91. c. If Betty plays 150 games of Ulose, about how many do you expect her to win? 10570 01%; [0'17ch/1573 =— ('IOXISU) d. Suppose that Betty will start out with \$500. if she plays 1509ames of Ulose, about how much money you expect her to end up with? Stu. SWW}¢\* nﬁz Flavﬁm ﬁn 157)qu slut “(£th («mm = straw 1+ as shall we #00 W’ ’W Weep [email protected] e. If Betty plays 150 games of Ulose, what' IS, the highest percent of the games you could reasonably expect her to win? W =“0 SD= 0—52: (‘3‘?) .000 b at . 07- 9‘ MW pug/Li vs a \$175 abwem Wm.” - 10 + L(oz‘l\ =- .N3 2: 1448070 — f. lf,Betty,wins-the-higheereasonablepercentefromAquestione(e)7,showemuch would her total gain be? Hi X“? 0+ l5?) 5W ; (149)0570 z: 119W S“ M I LLa/vtd [cs—e. “5° 22. 312:3 7,7. eBMsz7~ﬂlS¥ wnnlj a} ﬁEY‘L] [WW3 .13 965W 12.&X(*%)=_. _,___,,_ 4. Ace is playing Ulose, but he will only play 3 games. The chance he will win one of the games is 10%. The games are independent. a. Find the chance that he will win all three of the games. (.io)(.io)@al) = . col = 0.1% b. Find the chance that he will lose all three of the games. 0 -. l0)<_[-,l0) (l~. 10) = .710 =11ﬁ°7o c. Find the chance that he will win exactly one of the three games. (A030- to) (i -. m (a) = ,zw= 7—9. 3 Q0 5. Last year there were 7424 degrees conferred at SF State. 14.2% of them were in Humanities. Professor Chalkdust will get a simple random sample of 80 of the degrees and ﬁnd the percent in the sample that were in Humanities - a number he will call 13. a. Find the mean (p) of j} W = 141)?" b. Find the standard deviation (0') of p, {PU—P PS _ (.l Hall—ultra, W1 1» o'b‘l"@ V‘ ' S’o b. Find the margin of error of Chalkdust’s sample percent. (ZULM‘Q 2 - 0" 3" 6% c. Would you be surprised if 11% of the degrees in Chalkdust’s sample were in Creative Arts? Answer“ es” or “no” and ex lain wh or wh not. . Y P V y (4“ d M Q W No.l1WoA4,bMWlSDWMW lSD ﬁWW§. W15 M wkod’w‘e W‘Pui' +03%. 6. There were only 1000 degrees conferred at Declineto State. But the percent in Humanities was the same as at SF State - 14.2%. How big should a sample of degrees from Declineto State be in order for it to have the same margin of error as Chalkdust’s sample from SF State? W SW siz—er YO. Math 124.13 Spring 2011 Helen. F inkelstein Midterm #2 - April 7 1. Here are the responses of 240 students-to a survey. The question was, “Do you think 8 am classes should be eliminated?” The responses are shown separately for the men and the women. opinion yes no totals _ sex male female total MAL: £19.- : 50‘?!) c. Describe the association between opinion and sex. Maﬁa/”wane shy/0% WWH SajW (gaunt/W SWA MWaﬁd. 2. In the game of Craps, the chance that a player gets the combination called “craps” is about 1 1%. a. Find the odds that a player will get “craps." l- .H= «3’17 O , v“ MA— 199 as .lZ b. Find the chance that a player will not get “craps.” 1"!” t ‘g/ﬁ2ﬁ8ci‘vo 3. Betty is gambling, playing a game called Ulose. The chance she will win the game is 20%. If she wins she will gain \$8. If she loses, she will lose \$7 (for a gain of —\$7). The different games she will play are independent. a. Find the mean (expected value) of Betty’s gain. f“ \$67») + (-1)(.&o)= Lb «5.4, = @ b. Find the standard deviation of Betty's gain. 0‘ = (“C—MY“ (.20) + (:11 - («ML (.90) 3/ 12107-03 + (—332 (-80) = .139 .— c. If Betty plays 70 games of Ulose, about how many do you expect her to win? 109° it ‘10 3W= C-wlé‘wl @@ d. Suppose that Betty starts out with \$500. If she plays 70 games of Ulose, about how much money would you expect her to end up with? Ski 5W ”’5‘; M ft: \$91 {39/ij (\$190620): \$2.90- 1} SM 3w: Wm \$7500 ml lost. ﬁ. 280 all an m but QM Z 2. 0 e. If Betty plays 70 games of Ulose, what is the highest percent of the games you could reasonably expect her to win? H’ﬁw PAW/[j 1‘s 2 SD’; about, WW: ,20+ 260”?) " oLQG [email protected] f. |f.Betty,wins,the,highestteasonablepercentjromguestion,(e)r,,howemuch*# would her total gain be? Shwwkétm‘m 2912622 “F 70 Jot/mum, 02.963610): Zlga/uUbb Ska N‘DMM WM llama—Md. [032. 70-21—- 9‘! 3W win 7-1 glitch/u 2t"-%’= \$169 105”}9‘1 adj, km (Mag-,3: «\$32.9 4. Ace is playing Ulose, but he will only play 3 games. The chance he will win one of the games is 20%. The games are independent. a. Find the chance that he will win all three of the games. CLX‘ZXLV " '00 8 a 0.896 b. Find the chance that he will lose all three of the games. (i v-l)<l-.23(\v.7—) = . 6’12.-— 51.2% c. Find the chance that he will win exactly one of the three games. (-700 —. L3 0 —-.z) (3) 1.3 34 a- 5. Last year there were 7424 degrees conferred at SF State. 18.7% of them were in Creative Arts. Professor Chalkdust will get a simple random sample of 200 of the degrees and ﬁnd the percent in the sample that were in Creative Arts ~ a number he will call 13. a. Find the mean (u) of I“; W = P T" ‘33—) 670 b. Find the standard deviation (0') of 16 Cl— 3 l _ ' ,_ (SD 3‘] LTX'P' “2 (”72931-73 “l-Mo '15 “’6 52.79 ‘® b. Find the margin of error of Chalkdust’s sample percent. (z)(.ons‘)x .o 5’5‘ =- c. Would you be surprised if 21% of the degrees in Chalkdust’s sample were in Creative Arts? Answer “yes” or “no” and explain why or why not. No. 2:126 4;. mm m MW 4 42% ~ am ~ mm It is W lSDalrm‘l’lvamu SOW‘IS WwWWM/M +05%. 6. There were only 1000 degrees conferred at Declineto State. But the percent in Creative Arts was the same as at SF State - 18.7%. How big should a sample of degrees from Declineto State be in order for it to have the same margin of error as Chalkdust‘s sample from SF State? W4 SW sip: — 2’00- ...
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solutions_to_second_midterm[1] - Math 124.13 Spring 2011...

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