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SampleMidterm_Solution_f10 - Stat 3011 Spring 2010 Midterm...

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Unformatted text preview: Stat 3011, Spring 2010 Midterm Exam 1 Section 1: Multiple Choice (8 Questions, 3 points each) For the multiple choice questions, circle one of the listed choices for each question (no explanation is needed). 1. Assume the number of calories in a McDonald’s Big Mac follows a bell—shaped distri— bution, with a mean of 576 and a standard deviation of 18. Then approximately 95% of Big Macs have (a) Between 567 and 585 calories (b Between 558 and 594 calories etween 540 and 612 calories ((1) None of the above 2. What is the sample mean of the following set of numbers: 28,15,25,19,18,18,23 3. Which of the following is a discrete quantitative variable? @ umber of people in line at a bank (b Height ) (0) Telephone number ) (d Time it takes to complete a homework assignment Stat 3011, Spring 2910 4. The probability equation P(A U B) = P(A) + P(B) holds: (a) For all events A and B (b Only if A and B are independent Only if P(A H B) = 0 (d) This equation never holds 5. The probability equation P(A 0 B) = P(A) =1: P(B) holds: (a) For all events A and B Only if A and B are independent (0) Only if P(A F) B) = 0 (d) This equation never holds 6 The probability equation P(A 0 B) = P(A) >1: P(B|A) holds: .For all events A and B )Only if A and B are independent (C) Only if P(A f") B) = 0 (d) This equation never holds 7. Joe Mauer’s 2009 batting average is: .A statistic )A parameter (1:) Neither a statistic nor a parameter 8. Which of the following is resistant to outliers? (b) Sample mean ((3) Standard deviation (d) None of the above 3/10 Midterm Exam 1 Stat 3011, Spring 2010 Midterm Exam 1 Section 2: Short Answer (2 Questions, 8 points each) Below is a boxplot representing the responses from our class survey to the question, “How much money did you spend on your last meal?” Dollars Spent on Last Meal Before Class Dollars Stat 3011 Students 9. List four interesting facts this boxplot tells you about the amount of money spent by students on their last meal before class. (One such fact is, “Exactly three students Spent more than $15”, but you may not use this example as one of your four.) ARSWUS Ma W9, bui— Comc‘t «sums hdwlt. HA. ¥ollowfiijfi o n+ let-15+ 0M. rum {A fin class SFen’r $0 on Hair lqsl‘ meal- . Tl“ Mul’tim s‘mxlr is around $6 of #7 dbllafS. ' Maud infill D‘l' WSMNS Srm’l lptlwan 433‘ $8 04 “HAW \aSJI Mal. . TL; J‘s-hilW-‘(im oi” Hm, dollavs stand fan last mal is Skewecl {9 He rials. 4/10 Stat 3011, Spring 2010 Midterm Exam 1 10. Would you expect the mean amount of dollars students spent on their last meal to be larger than the median or smaller than the median? Use the boxplot to support your answer. We slmll urccl -H,.a mean “manual” 0‘: clbllaa‘ sfmi in be lag «Hm ‘HJ. Mzollhn, Thu Lapin-l {alien-kg #2 ull‘slvibwlw‘on I‘S skewed +0 m ay’r. m raster "MM" is [oner ‘Hwn m Ie'Ft “Wham“, M1 am are am Mliers above $15“ mgr mu ,‘n‘Hq-le as mean, in fia-Cl” H4 Man o‘l‘ Hu's «lain :3 $6.75— (Incl H4 Melina {s 5i“, even. 5/10 Stat 3011, Spring 2010 Midterm Exam 1 Section 3: Completely answer each question. Show all work for full credit! Problem 11 (20 points total) About 5% of all pregnancies in the US. occur after fertility drug use. These drugs dramatically increase the probability of giving multiple births (twins, triplets, etc). Suppose that the chance of a pregnant woman having a multiple birth is 12% if she took fertility drugs but only 2% if she did not take fertility drugs. (a) (4 points) Draw a tree diagram illustrating the information given in the problem. 17’ Mun‘Ple Bir‘l‘LS Usdiulél‘rlj /83 ? Dfufls \vale g‘r‘n‘s (b) (4 points) Using the information given, what percentage of all US. pregnancies result in multiple births? Give your answer to the nearest 0.1%. Lei M : Euml as Mulfiple loiFHnS F: Edna pl Edam) #3 “SC 100; “MPVPCMF? I Mme-ma. PfMlF°)'PCFC) = Alf-05) + .ons) : 1006+ ,Olq = 0035—) 50 4‘52 GPA” “'5. fry-racks FQSMH I‘A mul'l'lfll LI‘I'HIS. 6/10 Stat 3011, Spring 2010 Midterm Exam 1 (c) (6 points) Randomly select one US. woman who just had a multiple birth. What is the probability that she took fertility drugs? (Hint: This is a conditional probability.) new): mom} = thM-PCF) PO“) PM) 2 3.1 (.05) ._ ‘ _ . ' ,OlS- '* ii TL; wabliflj llM'l' HMS War-Mn +wk Ming My :3 .14. (d) (3 points) Suppose we randomly select three pregnant U.S. women. What is the prob— ability that none Of these three took fertility drugs? IMF)”: .05, 5o FCF‘):,‘15' “Fa“ PC“ PC) 304‘?!me [Wilt .953: .357 ..._.————— (e) (3 points) Now suppose instead we randomly select three US. women who just had a multiple birth. What is the probability that at least one of these three took fertility drugs? 551le spam 5: §FFF. FFN. FNF, NFF, am, umwe NM} PCu‘l lcusi m i'vblfi Rwliliij 40(35): lfiFKNA/N) 8w? WL are jive-4 Hut “Ha. women Mani Mull-lec \aianS , SD WAD; PCF‘IM) : l‘P(FlN) 2 .710 so P(NNN) .~. (Wilfmlpnm) - [mam]; = (303:,ng 50 HQ al' leas‘l one took Fermi“) olmjs) = 1,..qu : 3—513]— 7/10 Stat 3011, Spring 2010 Midterm Exam 1 Problem 12 (22 points total) The instructor of a large political science class polled his students to find out if they are registered to vote and Whether they prefer Democrats or Republicans. The results of the class survey appear in the following contingency table. Assume every student in the class took the survey and answered both questions. Registered to Vote Yes N o 75 1 10 Total Prefers Republicans Prefers Democrats Total (a) (4 points). Suppose we select a student from the class at random. What is the proba— bility he or she prefers Democrats to Republicans? 1H: CL .S MOIPQ ms was: “a r c is 2 a, w. u Tblal -——-——-- (b) (4 points) What is the probability the student prefers Democrats to Republicans and is not registered to vote? Wfrefus ans an). AM fiasislmé l1: Vale.) Bit Prefers Dams anal Nri’ Egjis'leral * Tolul '— ~— 3:1 8/10 Stat 3011, Spring 2010 Midterm Exam 1 (c) (4 points) What is the probability the student prefers Republicans, given that he or she is registered to vote? {Br R: Event Prefers Rapublimnj \f” Eueni’ (raglan! in Voic PCRHV)‘ 172.22 = .33: _ PW) "— mug/1”, lfi’S ‘ 0 17(05- __.__—-—. New) = (d) (4 points) What is the probability the student is registered to vote, given that he or she prefers Republicans? incl/ms mm): film : 15;.“ PCR) “17:2. ‘10 _ .8233 (e) (6 points) Are the events “prefers Republicans” and “registered to vote” independent in this political science class? Justify your answer numerically. dick: is Ptanvy=a©~P£v37 ‘75- Ptaml)‘ 33w. ) Pea—Parr :19;- 123= 33% :333 mi) arfi (Total, SD +112 {NC-Ab are [‘Adefltlkdlfll‘. Allumiw‘vclfl , we can deck FCRN3=PUQ 0r PCVlRVPN). We, wi\\ ghd EtiMQlfb W1 Cad“ Case. 9/10 Stat 3011, Spring 2010 Midterm Exam 1 Problem 13 (18 points total) The following stem—and—leaf plot represents the number of points scored by LeBron James in 54 NBA basketball games this season: 22444 | | | 12233334 I 5555667788999 I 1222222334444 I 566667778 I 0134 I 78 vbI-PWUJMMl-‘I—k (a) (6 points). Is the number of points scored by James a categorical, discrete quantitative, or continuous quantitative variable? Diwali»; T4m¥i~a1106 3 [411114 possible Valufls am lac lis‘l‘ltl‘ (b) (6 points) Explain why one row of the stem—and-leaf plot does not have any “leaves”. 171,111" rcw‘ 15 FQSCNQJ gr {51161 feinl’ jaMfl—SJ mul— L6 Eran 1105 no‘l‘ Scorecl 1,1}qu If m1 1‘! in 93 34mg +113; 564304- (c) (6 points) Compute the median number of points scored by James in his 54 games this SBELSOII. TL; number 91732445 13“” is even, 513 lair-e +14 quemje oil H4 797151 61ml 23-h star-la; “dues: 31-123,? ‘— 515— _._.___ 10/10 Stat 3011, Fall 2010 Sample Midterm 1 Problem 14 (15 points total) According to the November 5, 2009 Star Tribune, 36% of all Americans ages 18 to 35 have at least one tattoo. (3.) (7 points) Suppose that 39% of all Americans ages 18 to 35 who have at least one tattoo also have at least one body piercing. What is the probability that a randomly chosen American age 18 to 35 will have at least one tattoo and at least one body piercing? Del-Mt meals Tomi Bplwlwe Tr: gfmsm [acts al‘ leas‘l' mt. halite; g? : irfion lmxS Al'— quSl— 0M L013 flerclnj'i 1m PCmB?) = FCfiPlfl'l’m '-‘ 3‘? 23¢; = .l‘loLl (b) (8 points) Suppose we randomly sample 5 Americans ages 18 to 35. What is the probability at least 3 of them have at least one tattoo? 42+ X a. m War was We at 5‘ at. Am. out least ML W0- TL!» X" 5:4(3136), Pea-:3) WW3) WM) +PCx=§l am a We at is Jon, 906:3) =(§).363(t-,35)"’: .mu 90H) = (t) tau—30* = .0537 “F53 -.—. Cir) $670.36). : ,0060 50 F003); .l‘ill+.os37+,oocoo= ,AS‘os 10/10 ...
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