answer_key_sec_4 - AEM are Name: Mower Springr 2008...

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Unformatted text preview: AEM are Name: Mower Springr 2008 Section: ll? “ Section 4 l.) A production manager has eleven people in his crew. A special project that will @ require five people for about a week has been assigned to this crew. Since any of the eleven people could successfully serve on the special crew, the manager wishes to select the crew randomly. How many different possible five-person crews can he select from the eleven people? ( W) 'n I, Ill : (,3) EYE: 111v} 2.] A restaurant has collected data on its customers’ orders and so has estimated ILL empirical probabilities of what happens after the main course. it was found that 50% had dessert, 40% had coffee only, and 30% had dessert AND coffee. Pun=-§‘ Plcrrcliii+ rvrancjv.5 a.) Draw a Venn diagram for this situation. It 3-3) p c. _ .13.} Find the probability of the event “had coffee." “4' Fir): fiat/+3.4“ .c.) Find the probability of the event “did NOT have dessert.” "it W 1d[.}r.§)J.-5/ .} Find the probability of the event “neither coffee nor dessert." Wafer"): «l @ 3-] Find the prob.=3tl':-ilit5.F of the event “had coffee DR dessert." Lflw' [A D): 1" Ffp) L..- ; I griffn l3 :3“? ' {J Art" the events “had coffee“ and “had dessert“ mutually exclusive? How "Ll do you know?I ("l 3) _ H. “mm big; it? New brim c-Wi’ a, 1qu scrim -* Pfcrwbs‘c _ Mimi/g overlap in W W pinata/m» _ g.) Find the conditional probability of ordering dessert GIVEN that the H customer ordered oofi'ee. if?» PHIL): Hem-)3 ,3 9 egg? ._,,___—--1 _._- Pr’c} I?" h-] Find the conditional probability of ordering dessert GIVEN that the @ euStomer did not order coffee. '7 D o J a ‘3‘ L) ' ' if do) [[231 i” f-Wii" rte-.0 . :3 To see if coffee and dessert seem to go well together, compare your 1! ' answers to parts {g} and (b) above. in particular, who is more likelyr to order dessert; a eustorner who orders coffee or one who does not? A» dilemma” rim (wrest MW 3.} The following table summarizes data on smoking status and perceived risk of smoking and is consistent with Summary quantities obtained in a Gallup Poll conducted in November 2‘3021 L N) _ Perceived m T Very Somewhat Not Too Not at All _ Smokin Status Harmful Harmful Harmful Harmful Pt. t) "- - y“ [ F? rial) _. ' “Isiah ‘33‘1‘ 5'10 H: ‘t 1245‘ Assume it is reasonable to consider these data as representative of the LLB. adult .._._F—- population. __ a.) What is the probability that a randomly selected LLB. adult is a former @ smoker? dial/qu ; I 3w}; _ _b.} What is the probability that a randomly selected LLS. adult views smoking H as very harmful? _ U) '9'?”/aae : 3W! e.) Wl'tat is the probability that a randomly selected LLS. adult views smoking @ as very harmful and that the selected individual is a current smoker? Was a a .351 as?! d.) What is the probability that a randomly selected U.S. adult views smoking Q9 as harmful or they are not a current smo(ker? ) rive am He) * r vast-’1 t": .: _‘}L,j(f.f_qu1Lffdl;'-f3 " r:- . of .1} q 5" e.) What is the probability that a randomly selected [1.3. adult views smoking u *- as very harmful given that the selected individual is a current smoker? Fits): fl .W‘f‘i‘ are) cases __f.) What is the probability that a randomly selected LLS. adult views smoking (if?) as very harmfirl given that the selected individual is a former smoker? rifts) -fl§i ears PIP) .asvt g.) What is the probability that a randomly selected US. adult views smoking “,j as very harmful given that the selected individual never smoked? :, :.' rw: Ff N) 1 15-11:; {I :36“ 4.) 11.} How do die probabilities computed in parts {e}, (t), and (3} compare? @ Does this surprise you? Explain. .L {L Mowers seat not ,. PMfiMpbiLyj It; v M WW3; Surpass mnsmows “mot 5”” “fl ' W'MW v In a certain country, men constitute 58% of the labor force. The rates of unemployment are 6.2% and 4.3% among males and females, re5pectively. Suppose a worker is selected at random from the country's labor force. What probabilities do the percentages above represent? (Use symbols such [F as M for male, U for unemployed and so EOHh.S W: WW I) 6.; WM): .95 Hosp; Jeweler!va ; so?“ aw) a} > .5? Hum): 1' who) r we #2" What is the probability a worker selected at random is male and unemployed“? ( '33) P l M H all) NM} New awn aw) .aasse c. What is the overall rate of'unetnployment in the country? We) 4 PM a bill a (w a a) e tsetse) warm) "' 0.3.55qu .sl‘flflla F - {J 571119 3” What is the probability a worker is female and employed? rtw r": w) «- WWW“ka {as}! as?) ’ WWI . e.) If a worker, selected at random, is found to be unemployed, what is the I probability]r that the worker is a woman? -: Hostile}: :r 5' flu?) .oeHfi'f ' .sZJLm/ fix) 5.] A list of important customers contains 25 names. Among them 20 have their accounts in good standing while 5 are delinquent. Two persons will be selected at random from this list and the status of their accounts checked. Calculate the probability that: a) Both accounts are delinquent. J. W ( sissy? tan) a 45335 I __b.) One account is delinquent and the other is in good standing. Q91 {coups/M) r {MMWMJ 3 too e .zw a .3243 6.] Ranox Construction has bid on three major construction projects, all of which are due to begin in die spring. Ranox needs to begin stockpiling certain materials and building up its labor force right away if it receives any of the contracts. Due to the absence of planning in the past, Ranox has lost sizable amounts of time and money. The extent of the required buildup depends on the probabilities of the number of contracts it receives. The president ofRanox estimates that the probability asscciated with receiving contract A is .Ej contract B is .fi, and contract C is .4. [Assume that all events are independent.) states PIPJ'W ride-v Us} 1|tl'r'hat is the probability that the firm will receive all three contracts? ti rte n a tic) -' Misfit ‘1‘)" M? b.) What is the probability that the firm will receive none of the contracts? t’ l et— a tit-n63 5 (tensity): W 1What is the probability that the firm will receive exactly one contract? c.) 69 am mat-inc"): 1‘ tin-axe} - my k Plfif’nflrt’lLLD-i (fissile) = hi?“ / x3457 Prn‘ :4 sin e) a {lM-st-‘r‘l' 10?} @d.) What is the probability that the firm will receive at least one contract? 11%ka. ffnblé) ;: l“ F{fl'fl' n, 3914 bl“) r. was a ear T.) A company that manufactures video cameras produces a basic model and a deluxe (9 mode]. Over the past year, 4fl% of the cameras sold have been the basic models. I 1 Of those buying the basic model, 30% purchase an extended warranty, whereas 513% of all purchasers of the deluxe model buy an extended warranty. If you learn that a random]? selected purchaser bought an extended warrantyj what is the probability that he or she has a basic model? If?“ ELF} ...
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