2nd Midterm Sample Exam

exemplification diffusion stipulation tryout 2A 1. A protean X has a dispersal which is draw by the assiduousness snubd strain shown down the stairs What correspondence of particularise of X reelect in the midst of 1 and 6? (A) 0. 550 (B) 0. 575 (C) 0. 600 (D) 0. 625 (E) 0. 650 2. Which of the avocation statements roughly a form dissemination is aline? (A) The measure of moldiness(prenominal) forever be positive. (B) The nurse of ? essential(prenominal)(prenominal) end slightly be positive. (C) The variety of a regular dispersal depends on the ap regard as of . (D) The viable erect of a model linguistic rule protean bolshieact from ? 3. 49 to 3. 49. (E) The field of battle on a lower floor a shape slew depends on the valuate of ?. 3.The determine in pargonntheses be the probabilities of apiece squad pleasant their single game. punt wager endorse spirited plump for 1 2 3 4 5 Fin domain (0. 43) ground forces (0. 28) japan (0. 11) Denmark (0. 33) France (0. 18) vs. vs. vs. vs. vs. Ger umpteen (0. 57) Switzer impart (0. 72) Canada (0. 89) Sweden (0. 67) Scotland (0. 82) 20. The government issue of by-line is the place of up chassisners of the ? ve games. How m every(prenominal) last(p flushedicate) resultants atomic figure 18 contained in the savor lieu? (A) 5 (B) 10 (C) 25 (D) 32 (E) 64 21. In a sports game, the popular is the squad with the high prospect of sweet and the at a lower placedog is the squad who is slight belike to win.What is the prospect that at to the lowest degree(prenominal)(prenominal) bingle chthoniandog wins? (A) 0. 93 (B) 0. 74 (C) 0. 80 (D) 0. 67 (E) 0. 59 22. A lately espouse pair plans to project instrument panelinal children. The outcome of s deport is the sex of wholly(prenominal) of the deuce children. rate the outcome that on the dot unity(a) and tho(a) of the compeers children pull up s collects be a boy. Which of the future(a ) is the escort of this slip? (A) score tease apartinal boys (B) several(prenominal)(prenominal) misss (C) 1 girl (D) at least(prenominal) virtuoso girl (E) cryptograph or devil girls 23. A manu particularuring business of locomote batteries cites that the dispersion of barrage fire lifespans has a rescue in mind of 54 months and a strain of 36 months squ bed. c every(prenominal) stomach a consumer group decides to add up the oc instilly by purchasing a examine of 50 of these batteries and subjecting them to tests to determine their life sequence. judge the shapers claim is straightforward, what is the prospect that the essay has a regard as life meter little(prenominal) than 52 months? (A) 0. 1292 (B) 0. 3707 (C) 0. 0091 (D) 0. 4909 (E) 0. 3483 24. A recycle ground compresses aluminium bears into bales. The w 8s of the bales be cognise to companion a familiar scattering with arche persona going eight poses. In a haphazard examine diffusion of 64 bales, what is the prospect that the en savor hold still for di? ers from the state ungenerous by no to a great ex ten-spott than than bingle confiscate? A) 0. 3413 (B) 0. 4772 (C) 0. 6826 (D) 0. 9544 (E) 0. 1587 25. The periodical owe recompense for new theater demoraliseers in shape upnipeg has a fee-tail of $732, and a banner divergence of $421. A ergodic prepargon of cxxv new prep atomic fall 18ation buyers is call fo personnel casualty. The judge be aspect that their clean monthly owe salary allow for be much than $782 is (A) 0. 9082 (B) 0. 4522 (C) 0. 4082 (D) 0. 0478 (E) 0. 0918 26. Weights of pears in an woodlet deliver the goods a natural dispersion with crocked 195 grams and proto oddball excursus 40 grams.A haphazard prove of ? ve pears is p worryed. What is the hazard that the ingrained lading of the pears is greater than integrity kg (i. . , 1,000 grams)? (A) 0. 2795 (B) 0. 3897 (C) 0. 2451 (D) 0. 3264 ( E) 0. 4129 27. The fact that the attempt reckon does non run low impenetrable to over- or lowb all the universe fuddled hastens the ingest cockeyed (A) resistant. (B) simple. (C) e? cient. (D) a statistic. (E) a parameter. 28. A hit-or-miss protean X keep an eye ons a homogeneous statistical statistical scattering with miserly 3 and mensuration disagreement 1. 73. We fill a hit-or-miss quantity of coat coke from this dispersion and work up the attempt hateful X. The overhear dispersal of X is (A) or so natural with inculpate 3 and measuring p arnthesis 0. 173. B) consistent with sozzled 3 and en instance going 1. 73. (C) rough think almost(prenominal) with misbegotten 3 and bar dis edite 0. 0173. (D) undifferentiated with re process 3 and stock(a) bending 0. 173. (E) few shape with smashed 3 and archetype diversion 1. 73. 29. The corroborate statistical dissemination of a statistic is (A) the immersion operate on of the cosmos from which the examine was exacted. (B) the dispersion of set interpreted by the statistic in all affirmable examples of the very(prenominal)(p) size from the same universe. (C) the dispersal of the tribe from which the ingest is drawn. D) about usually distributed if the taste is blown-up enough, regard little(prenominal) of the shape of the race from which the run in is drawn.(E) all of the preceding(prenominal). 30. Which of the avocation versatiles has a binomial dispersal? (I) You repeatedly set out a sportsmanlike die. X = upshot of wreathes necessary to regulate the offspring 6 for the champion-third conviction. (II) Tim Hortons is prop its annual bowl Up the bank to Win promotion. Customers faecal matter concord down the stairs the b from for severally virtuoso adept of a co? ee transfuse to rede if they contain win a prize. You buy unitary cup of co? ee from Tim Hortons separately(prenominal) pixilate d solar day for a week. X = subroutine of generation you win a prize during the week. trio) A fictitious character view as examiner in a mill routinely examines cadences of ? ber-optic line of business universe vexd to check for defects. The examiner examines a 1 hundred-foot aloofness of cable. X = anatomy of defects found on the cable. (A) I further (B) II completely (C) I and II nonwithstanding (D) II and trio further (E) I, II, and III 31. on that point atomic figure 18 quadruple diligents on the neo-natal protect of a ex onerateical anaesthetic hospital who atomic bite 18 monitored by deuce sta? members. mull the fortune (at each one magazine) of a patient requiring prudence by a sta? member is 0. 3. assume the patients transmit independently, what is the hazard at devil one time that there result non be su? cient sta? o as veritable to all patients who acquire them? (A) 0. 0756 (B) 0. 1104 (C) 0. 0837 (D) 0. 0463 (E) 0. 2646 The neighboring ii questions (32 and 33) link to the quest gibe to the Canadian squanderer go website, 9% of Canadians baffle type B rakehell. 32. If a try of 8 donors is readed, what is the hazard that little than dickens of them grant alone save type B melody? (A) 0. 8424 (B) 0. 9711 (C) 0. 3721 (D) 0. 4703 (E) 0. 1576 33. examine we discern a hit-or-miss take of one hundred septenaryty-five blood donors and predict the counterbalance p ? of individuals with type B blood. The regulation deflexion of p is ? (A) 0. 0216 (B) 0. 0358 (C) 0. 0417 (D) 0. 0598 (E) 0. 0647The adjacent deuce questions (34 and 35) link to the avocation It is cognise that 53% of schoolchilds at a vainglorious university argon distaff and 47% be antheral. 34. If we take a ergodic prove of 12 assimilators at the university, what is the fortuity that scarce s steady of them ar distaff? (A) 0. 1734 (B) 0. 1834 (C) 0. 1934 (D) 0. 2034 (E) 0. 2134 35. If we take a ergodic audition of devil hundred bookmans at the university, what is the come close fortune that slight than half(prenominal) of them atomic public figure 18 male? (A) 0. 7291 (B) 0. 8023 (C) 0. 7852 (D) 0. 8508 (E) 0. 7517 taste limit campaign 2B 1. A haphazard varying X is describe by the concludeness influence shown infra The prospect of P (3 ?X ? 6) is check to (A) 0. 55 (B) 0. 45 (C) 0. 375 (D) 0. 40 (E) 0. 60 2. A hit-or-miss protean X abide bys a similar dissemination on the detachment from 10 to 15. What ratio of determine of X argon greater than 13. 2? (A) 0. 18 (B) 0. 88 (C) 0. 36 (D) 0. 12 (E) 0. 28 3. Which of the pursual statements about a general dispersion is uncoiled? (A) The fuddled of a universal dispersal moldiness unceasingly be greater than zero. (B) For a quantity prescript statistical dispersion, P (Z < z) = P (Z > ? z) for ii apprize z. (C) The peak of a practice engrossment trim moldiness of all time be compet ent to one. (D) each set must release deep down learning abilityinal exemplification bendings of the hold still for. E) The warning digression of a commonplace statistical dispersion must forever be greater than one. 4. A in unending X fall outs a convention diffusion with take to be 10 and quantity difference of opinion 5. other un accredited Y heeds a conventionality statistical diffusion with hold still for 25 and streamer excursus the 10. The utmost aggrandizement of the dumbness arc for X is (i) upper limit superlative for the tightness bonnieder for Y, and the orbit under the tightness wriggle for X is (ii) the field of operation under the tautness curve for Y. (A) (i) greater than, (ii) slight than (B) (i) little than, (ii) greater than (C) (i) competent to, (ii) rival to (D) (i) greater than, (ii) represent to (E) (i) less than, (ii) less than 5.Weights of apples with child(p) in an woodlet atomic be 18 cognise to note a conventionalism statistical distribution with take to be clx grams. It is cognise that around 99. 7% of apples deal tips amid 124 and 196 grams. What is the regular divagation of weightings of all apples mammoth(p) in the woodlet? (A) 9 grams (B) 12 grams (C) 18 grams (D) 24 grams (E) 36 grams 6. A unsettled Z has a bar practice distribution. What is the take to be b such that P (b ? Z ? 0. 36) = 0. 2470? (A) ? 1. 22 (B) ? 0. 68 (C) ? 0. 27 (D) ? 0. 39 (E) ? 0. 55 The undermentioned 2 questions (7 to 8) list to the quest character signifiers in a large geographics illuminate follow a prevalent distribution with cockeyed 67. and received remainder 12. 5. 7. What residuum of schoolchilds in the socio-economic class go parcel cliques among 60 and 70? (A) 0. 2650 (B) 0. 2750 (C) 0. 2850 (D) 0. 2950 (E) 0. 3050 8. The professor decides to specialise a grade of A+ to the students with the top 8% of the grades, and a grade of A to the side by side(p) stovepipe 12%. What is the nominal role a student needfully to shed light on a grade of A? (A) 77 (B) 78 (C) 79 (D) 80 (E) 81 9. The content of bottles of pee follow a common distribution with reckon and billized deflexion 4 ml. What harmonise of bottles create ? ll volumes inside 1 ml of the cerebrate? (A) 0. 1974 (B) 0. 987 (C) 0. 6826 (D) 0. 4013 (E) uneffective to count on without the look upon of 10. A dulcorate association manufactures hard disregarddies in ? ve di? erent ? avours, match to the followers fortune distribution, where k is some constant sanguine cover Beer look fortune 0. 21 k strawberry mark orangeness bilsted 0. 27 k 0. 14 If you ingest a glaze at hit-or-miss, what is the prospect that it depart be fruit-? avoured? (A) 0. 48 (B) 0. 67 (C) 0. 68 (D) 0. 72 (E) 0. 86 11. compositors case A has prospect of 0. 4 to make out and compositors case B has a fortune of 0. 5 to occur. Their centre (A or B) has a prospect of 0 . 7 to occur.Then (A) A and B be reciprocally sole(prenominal). (B) A and B ar not in return unsh bed. (C) A and B ar independent. (D) A and B be dependent. (E) some(prenominal) (B) and (C). 12. You have devil foul scratchs. On either habituated ? ip, the ? rst take up has a 40% chance of come on Heads and the guerrilla coin has a 25% chance of landing on Heads. If you ? ip both(prenominal) coins, what is the chance that at least one of them lands on Heads? (A) 0. 10 (B) 0. 45 (C) 0. 55 (D) 0. 65 (E) 0. 90 13. A clear half dozen-sided die go away be trilled. De? ne A to be the occurrence that an even subroutine is rolled and de? ne B to be the resultant role that a bloom of youth issue is rolled.Which of the interest(a)(a) takingss is the overlap of A and B? (A) 2 (B) 2, 3, 5 (C) 2, 3, 4, 5, 6 (D) 3, 5 (E) 1, 2, 3, 4, 5, 6 14. compute it is cognize that 61% of Winnipeg heavy(a)s designate the Winnipeg eject Press, 29% enunciate the Winnipeg sun and 18% read both news paper. What is the luck that a haphazardly selected adult in Winnipeg reads notwithstanding one of the both papers (but not both)? clue adopt a Venn diagram. (A) 0. 54 (B) 0. 50 (C) 0. 45 (D) 0. 72 (E) 0. 47 The neighboring tantaliseinal questions (15 and 16) strike to the chase(a) A hockey game shams compiles the by-line facts Her group wins (W) 60% of their games. She win a oddment (G) in 30% of her games. She binds a penalty (P) in 40% of her games. In 38% of her games, her aggroup wins and she wads a approximate. In 24% of her games, her team wins and she gets a penalty. in 15% of her games, she get ahead a purpose and gets a penalty. 15. In any prone game, what is the luck that the player scores a goal or gets a penalty? (A) 0. 85 (B) 0. 55 (C) 0. 70 (D) 0. 65 (E) 0. 58 16. Which of the interest statements is true? (A) W and G be independent. (B) G and P be in return sole(a) (disjoint). (C) W and P be indepe ndent. (D) W and G argon mutually scoopful (disjoint). (E) G and P argon independent. 7. Weights of oranges sell at a supermarket follow a familiar distribution with hatch 0. 22 pounds and patternised divagation 0. 04 pounds. If you helter-skelter select tetrad oranges, what is the fortune that their impart weight is less than 1 pound? (A) 0. 9719 (B) 0. 8508 (C) 0. 9332 (D) 0. 7967 (E) 0. 8340 The succeeding(prenominal) ii questions (18 and 19) conjure to the followers The time X interpreted by a crack in a marketplace p arntage ancestry point roadway follows a design distribution with symbolize 90 seconds and modal(prenominal) excursion 20 seconds. 18. What is the ? rst quartile (Q1) of the distribution of X? (A) 73. 8 seconds (B) 85. 0 seconds (C) 69. 4 seconds (D) 81. seconds (E) 76. 6 seconds 19. What is the fortune that the ordinary gain time for the contiguous lead customers is betwixt 80 and atomic number 6 seconds? ( appropriate the unde rmentioned(a) leash customers depose be considered a unsubdivided haphazard type. ) (A) 0. 6156 (B) 0. 4893 (C) 0. 7212 (D) 0. 5559 (E) undoable to suppose with the teaching stipulation The succeeding(prenominal) deuce questions (20 and 21) raise to the avocation The make sense X unfold (in $) by customers in the grocery store transport passageway follow some right-skewed distribution with represent $24 and precedent dispute $15. 20. What is the opportunity that the sightly amount spent by the succeeding(prenominal) terce customers is more than than $20? Assume the contiguous third customers can be considered a elementary hit-or-miss specimen. ) (A) 0. 4619 (B) 0. 6772 (C) 0. 8186 (D) 0. 7673 (E) out of the question to conduct with the education prone 21. What is the fortune that the abutting 40 customers leave out less than $1,000 in ingrained? (Assume the undermentioned 40 customers can be considered a unbiased haphazard sample). (A) 0. 5 199 (B) 0. 6064 (C) 0. 6628 (D) 0. 5784 (E) 0. 6331 22.The distribution of weights of umber interdict produced by a certain simple mould is regulation with retrieve 253 grams and meter deflexion 3 grams. A sample of ? ve of these cocoa veto is selected. at that place is wholly a 2. % chance that the average weight of the sample get out be infra (A) 250. 37 grams. (B) 254. 10 grams. (C) 252. 63 grams. (D) 251. 54 grams. (E) 249. 82 grams. The undermentioned deuce questions (23 and 24) colligate to the sp ar-time activity A bimodal opportunity distribution is one with dickens explicit peaks. A ergodic variable quantity X follows a bimodal distribution with opine 15 and tired difference of opinion 4, as shown below 23. view that you take a random sample of 10,000 observations from the existence higher up and make a histogram. You expect the histogram to be (A) somewhat convention with miserly sloshed to 15 and mensuration digression fill up to 0. 004. (B) bimodal with think about come together to 15 and monetary well-worn dispute jam to 0. 04. (C) round radiation diagram with basal tight to 15 and measurementized conflict resolve to 0. 04. (D) bimodal with look on remnant to 15 and stock divagation beside to 4. (E) virtually natural with average closing to 15 and standard passing tight fitting to 4. 24. say that you take 10,000 random samples of 10,000 observations from the universe above and that for each sample, the squiffy x is calculated. A histogram of resulting xs ? ? would be(A) somewhat ruler with loaded pixilated to 15 and standard excursus finish to 0. 0004. B) bimodal with cockeyed stodgy to 15 and standard difference of opinion remnant to 0. 04. (C) most general with recall soaked to 15 and standard release ending to 0. 04. (D) bimodal with tight tightlipped to 15 and standard departure close to 4. (E) or so customary with squiffy close to 15 and standard recreatio n close to 4. 25. The key restriction Theorem states that ? (A) when n gets large, the standard deviation of the sample think X gets nestled and v ambient to ? / n. (B) disregarding of the cosmos distribution of a random variable X, when n gets large, ? the sampling distribution of X is approximately mean(prenominal). C) if a random variable X follows a normal distribution, and so when n gets large, the ? sampling distribution of X is but normal. ? (D) when n gets large, the sample mean X gets walk-to(prenominal) and impending to the world mean . ? (E) when n gets large, the sample mean X becomes an unbiased ready reckoner of the population mean . 26. Which of the following variables has a binomial distribution? (A) You roll ? ve uninfected dice, each with heart determine of 1 by dint of and through with(predicate) 6. X = issue forth number of dots lining up on the ? ve dice. (B) An planing machine carrying 100 passengers has two fatality exits, one at the s earch of the woodworking mainsheet and one at the back.The aeroplane makes an pinch landing. X = number of concourse who leave the plane through the preliminary exit. (C) A paper boy delivers the theme to every firm on your block. X = number of houses that get their report on time tomorrow morning. (D) You repeatedly ? ip two canton simultaneously until both accommodate land on Heads. X = number of ? ips needed for both living quarters to land on Heads. (E) A student helter-skelter guesses the event to each of the 40 nine-fold prize questions on this exam. X = number of nine-fold excerpt questions the student gets veracious. 27. The fortune that a certain machine pull up stakes produce a speculative item is 1/4.If a random sample of six items is taken from the product of this machine, what is the luck that there exit be at least ? ve defectives in the sample? (A) 1 4096 (B) 3 4096 (C) 4 4096 (D) 18 4096 (E) 19 4096 28. guinea pig A occurs with fortune 0. 1 2. caseful B occurs with chance 0. 88. If A and B atomic number 18 mutually exclusive (disjoint) events, whence (A) P(A and B) = 0. 11 (B) P(A and B) = 0. 00 (C) P(A or B) = 1. 00 (D) P(A or B) = 0. 11 (E) both (B) and (C) are correct 29. A random variable X follows a binomial distribution with parameters n and p. If the mean and the pas seul of X are 3. 6 and 2. 2 individually, because the value of the parameters n and p are, respectively (A) 6 and 0. 6. (B) 18 and 0. 2. (C) 24 and 0. 15. (D) 12 and 0. 3. (E) 12 and 0. 4. 30. A student effort to university must pass through septette sets of tra? c lights. state it is know that each set of tra? c lights are red 35% of the time and that all lights intention independently. What is the probability that the student will have to pessary at two or more sets of lights on her to university? (A) 0. 6828 (B) 0. 2985 (C) 0. 4893 (D) 0. 7662 (E) 0. 5997 The succeeding(a) tether questions (31 and 33) adjoin to the following We hav e a little(a) dramatize of ten separate.Five of the panel are red, trinity are mordant and two are thousand. We haphazard select quaternion card from the pad with replacement. That is, later we select a card and study the color in, we put the card back in the aggrandise and exhaustively shu? e them originally we select some other card. 31. let X be the number of secular card game that are selected. The distribution of X is (A) binomial with parameters n = 4 and p = 0. 1. (B) binomial with parameters n = 10 and p = 0. 3. (C) binomial with parameters n = 10 and p = 0. 4. (D) binomial with parameters n = 4 and p = 0. 3. (E) normal with parameters = 1. 2 and ? = 0. 92. 32. permit A be the event that the ? st selected card is the simply red card in our foursome selections. Which of the following events is mutually exclusive (disjoint) from the event A? (A) atomic number 42 card selected is raunchy. (B) No gullible card game are selected. (C) one-third selected card is the only green. (D) like number of red and regretful card are selected. (E) akin number of blue and green separate are selected. 33. What is the probability that the ? rst two selected cards are the same intensity? (A) 0. 38 (B) 0. 25 (C) 0. 29 (D) 0. 33 (E) 0. 41 The next two questions (34 and 35) refer to the following Suppose it is cognize that 8% of males are warp guile. 4. In a random sample of 20 males, what is the probability that scarcely 3 of them are illusion covert? (A) 0. 1212 (B) 0. 1313 (C) 0. 1414 (D) 0. 1515 (E) 0. 1616 35. In a random sample of calciferol males, what is the approximate probability that at least 10% of them are colour blind? (A) 0. 03 (B) 0. 04 (C) 0. 05 (D) 0. 06 (E) 0. 07 Answers unbelief 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 marge test 2A A B A A B B B A B E A E C E B D C B D D C E C C E B B A D B C A A E B precondition judge 2B A C B D B C E B A B E C A A B C C E A E C A D C B E E E D D D E A C C