Stats 100A Midterm 1 Example - Stat INA-lotro Probability...

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Unformatted text preview: Stat INA. -lotro Probability Midterm l .I. Sanchez UCLA Department of Statistics MULTIPLE CHOICE QUE-SHONE. ONLY ONE ANSWER ISCDRRECT. CHOICE MUST BE NHRKED UN THE SCANTRDH, AND ALSD HERE ON THE. EXAM. ONLY THE SEANTRDN 1liliilLL BE GRADED. NO WHILE UN SCfiNTRDN OR MORE THAN ONE MARK WILL RESULT IN 1} PUINTS FOR THE QUESTION HGT MARKED, EVEN IF IT IS MRKEII ON THE Exam. You may use the space near the question for scratch work. but scratch work will not be read. Question 1. A manufacturing company has two retail outlets. It is known that 30% of all potential customers buy products from outlet l alone. 50% buy from outlet 2 alone. 10% buy from both I and 2. and lflfi: buy from neither. Let A denote the event that a potential customer. randomly chosen. buys from outlet I. and let H denote the event that the customer buys from outlet 1. Which of the following statements is true‘?I ,_ t. eieo=o3 \ X [b)Pi{t4I"iH}‘=fl 3" '5“) erasuet=ot i :fiwss of} = as {fit-3f ta Pia u or = as Qflfififlfl 2. Set-ten applicants have applied for two jobs. How many ways can the jobs be filled if there are no djlferences between Ihejobs‘? .flth' ' {If a {is 4: [cl 4? id) 7 [e] 2 Question 3. Police rcport that TEE: of drivers stopped on suspicion of drunk driving are given a breath test. 35% a blood test. and see both tests. What is the probability that a randomly selected D‘t‘v'I [Driving 1|t‘r’hjle Intoxicated} suspect is given none of the tests? {a} ll? . x: ml 3M- n (to filo-I": "i l: _i l ' c4 {cl {Hid ‘ t..____ __.»'/ to not tel 1184 Question IL An insurance company believes that people can be divided into two classes: moss who are accident praise {A} and times Who are not {B}. Theirstatistics show that if aperson is aecidentlprone she will have an seeident [Cl at some time within a fitted l-year period with probability {14. whereas if a person is non-aecident prone this probability decreases to I12. We know that 3!} percent of the population is accident prone. The joint probability that a randomly chosen custonter is not accident prone and has an accident within 1 year is: . _ {a} e. 14' ““2. ts} chaise (c) not {a} u. 11 (c) ELSE- Queetlon 5. A manufacturing company has three out-of-town plants, A. B. and C. The plants are located in different cities. From among ten employees. three are to be selected to go to plant A. In hem-many ways can this selection be made? 3' is] 1000 l : ' ‘"" its] at» {He} no to] ass is] EBB Qnmflon IS. A customer visiting the suit department of a certain store will purchase a suit with probability {1221 a shirt with probability {13. and a tie with probability {1.23. The customer will purchase both a suit and a shirt with probability Ill]. both a suit and a tie with probability {114 and both a shirt and a tie with probability 1110. A customer will purchase all three items with probability tlflfi. Let A be the event that the customer purchases a suit. B the event that the customer putshasce a shirt and C the event that the customer psirchascs a tie. What is the probability that a customer purchases exactly one _ot'_ these items? '1: {a} ”I a" . . r [on its , eat} “it IE'I'III r._' -I Griu : {c} not IE1": a use so; l l - {e} DESK 116$th 'lr'. Ninety percent of all babies survive delivcty. However, 15 percent of all births involve Cesareant C} sections. and when a C section is perfonned the baby survives 92 percent of the time. if a randomly chosen pregnant woman does not have a C section. what is the probability that her baby survives? .~ “' '5'" Qli'bise be {a} 13.92 lb] 0159335 es ‘essa‘tx "5 t- a. id] 11345 {e} 1 Question 8. 0f the persons arriving at a small airport. mm H}! on major airlines. 30% fly on privately owned airplanes. and [(1% fly on commercially owned airplanes not belonging to an airline. 0f the persons arriving on major airlines. see are traveling for business reasons; the smreoporrding figures are 150% for persons arriving on private planes and 90% for persons arriving on other commercially owned planes. For a person selected at random from a group of arrivals in oorrtmereial airliners. find tire probability that the person is traveling on business. [a] 0.3153 {lo} 0.? {c} I113 ..--.-;... _ (a) diff; [e] are Question 9. Suppose a sampIe spam 5 emaists of 4 outeomes: S = [ a].oz.e3.ml. Which functions define a probability function? is] Plan} = infidel n 1.?th = Lima} =i it} Has = smog} = are.) = simian =§ in} Pics = was = late) = Leas =5 ref-rim} = was =- iflasi = Laos = i e:- Pta12r=éflszl=i.Pta3}=i.Ptasi=v} Question 10. In I988 the results of the Physicians‘ Health Study Research Group study were reported in the New England Journal of Medicine. in this study 2207] male physicians (aged from 40 to 84) were randomly assigned to two groups. One group took an aspirin every second day and the other group took a placebo. a pill with no active ingredient which looked just like an aspirin. The participants did not know whether they were taking aspirin or the placebo. After five years the number of participants in each group who had had a heart attack was recorded. The results are shown in the table found on this page. For male physicians aged 40 to 84. the risk of having a heart attack for those taking a placebo every second day is.. (a) twice the risk for those taking aspirin lb]: 0.3 the risk for tltose taking aspiring to] 0.55 the risk for those taking aspiring. {d} 3 times the rial: for those taking aspirin flier-1.013 the risk for most: taking aspirin titration 1]. What is the chance that among a grail: of four people chosen at random at least two were hunt in the same month {not necessarily the same year}. Mark your answer here and in the scantron. - tnfiefsrcs “a. . .__'_ ,;:, .3 ~'— --"' '- . ] ta ta .1 Eli) sass lcl 0.21% {d} on?! ' {e} llml Question 12. A system with E: independent components is such that the system will fail if at least one of the individual cmnponents fail. The probability that a component fails is 0.02. Let. A be tlte event that the system fails. How many outmmes of the sample space are in at? {all 0.114] {h} 0.035042 {c} 04 id} 46550 no ss__.'= Question 13. Suppose that you and a friend are matching balanced coins {i.e.. each coin has probability ill at landing head). Each of you tosses a coin. If the upper faces match and both are both head. you win 5.03 dollar, it“ they do not match. you lose 3.00 dollar [your friend wins 3.00 dollar}. If they match and they are both tail. you win 1 dollar. Let X be the random sample representing your winnings. Your expected gains and standard deviation are. respectively. _—._ _ I: ’ 'g't'i.r""l'r.1.~"- 112-13.“; {a} F“ 0.5: o“: 0.2 lb} y=01 rr= 3.00 {e} p=3:o'=0.5 '. {a} =0;o'=3-.3lfit5 {almanac Question 14. A tom: has lDtllJ people. 11m people can be classified by their income level and their education. with the following information: I 1112' have 516 years of sohoolittg and make 3- $50. III) I 30D have 3 it: years of schooling and make 3- $59,012!) I dill) have 5 16 years of sohooling and make 5 $50. fill). The joint probability that a randome chosen person has :r if: years of schooling and makes a» $5131 Gill] is (a) ill {bl 113? {cl 0.5 {at 11:45. {e} [3.62 Question 15. A doctor is studying the relationship between blood pressure and heartbeat abnormalities in her pa- tients. She tests a random sample other patients and notes their blood pressures (high. low. or neutral} and their heartbeats [regular or irregular]. She finds that: e 14% have high blood pressure. I 22% have low blood pressure. I 15% have an irregular heartbeat. I Of those with an irregular heartbeat, one-third hat-re high blood pressure. 1: Of those 1with normal blood pressme, one-eighth have an irregular heartbeat. What portion of the patients selected have irregular heartbeat and normal blood pressure? (“34% . _. H L H mm“ l 3' l :2. 3. . ' {at so 1‘1 :11 int !oo (also Question 16. It is known that 40 percent of the romantic dates that an adult has -while single are not much fun. No college students seeking a romantic partner decide to start going out independently on dates with other people chosen at random. to look forthe fun date out there. Find the probability that both of them find their first fun date in the 5th date. Mark your answer here and in the scantron. {a} 0.601 {b} 0.130255 "threesome {Hi Ami {e} HUSH?! Question 11. Let X denote it random 1irai-iahle that has the following piobahility mass function. -““ -IEIIiEIiEI at is the variance of X 'i' [mark yousr answer hct'e_end in the scentmn} mot F' —G.’1s0.i§=tf‘.1 [h] {3.51 I!” “'3 dim is low '31 'l-[FL +U.ir0.11fg_3-o.s‘ Quads-u 15. A system with 6 independent components is such that the system fails it‘ at least one of the individual oomponeuts fail. The probability that a compoth fails is llfll. Let A be the event that the system fails. What is the probability that the system fails? (Mark your answer here and in the seantron.) is} 0.93? {hi 13.3353 r h . L [cl 1 I Edi 0.543 @1111“ Question 19. 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