practice-exam1-421-s08solutions

practice-exam1-421-s08solutions - I Pmc—Huz £7an 4...

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Unformatted text preview: I Pmc—Huz £7an 4 K€‘~[ _ W. l. Fifty applicants interested in working for the Food Stamp pro designed to measure their aptitude for social work. Below is for the scores data- gram took an exnulinnlion the relative frequency histogram a. (7 pts.) Find the n'Iissing height over (70,80) and restore the frequency table l'or it. (make Hun: that the total nunllrcr of entries ill-your frequency table is 50)- ' I Sm 9.; J<‘\’\C re\_ Jill, _ I 2. gFEfipLencies Must Lac. 4 . €35 ~4<v\\€_ tun-55.x“ «ck. gweckumcy (S l 0.2.0 {00 Iv- (3 pts.) It is kuoWn that. ifu histogram: is positively Skl-chfll, tlurn (nominally) the mmm is gruutur than the (median, while if it: is negativ you rompzn‘o Lin: median with the Wu: C tux oly skewed, thou the motlizm is larger. (nt1 [noun for the given llih‘togrflnl? Which om: is greater? Lawreape 'Hu. M on; -‘<\u2 mcaxmm grace. +‘me histang {-5 shriemé +0 Arm 1&1?“ meofi_ Ag “’9‘: Jr‘--*--W\ 1* Luz mcchaxn. . __,._.. .. .—.-...J I -—-»— 2.(Jim-utho(artificial)datasol. ll}1 (2', It}, (.3, El, 3, I}, (i, H a. {ti .2 [-2 I 2 pts.) {'Julmllatu (2;,MJ33 (limit and [,hird quartiles and lumiiun). ArrmSc -\ "um Ci chi-a (p. t\.’\_cwens‘\1’\5 CWAGJF" @- 2 2. 6 ‘58\0 W? #4"; fiégb. ‘8’ J 9L, a» I’. (13.3 l 3 plan} Calculate the inlmrqum-tilu range {Hell} and poinl. out. outliers, if any (um- tin- IIiLa IQ“ ('l‘iiJEI'iUII)- K": (3555" :- (gr-2 :2 é; 3. (7 pts.) Create a set of 5 positive numbers (repeats allowed) that have median 10 and “19.3117. 0 o 10) IO) 1‘5 / / ___-—-- _,_.———_ ngo 32': o+o+\o+\0‘l"5 —.= 3.5.56! fli—‘fl 5 4. (7:2+5 pts.) For the following small data set Calculate mean it and standard deviation 3:- 32:. -k+‘8+1 : i=2: 3 3 1 a) 5:: J—( (:Lt_z)z. +(3,g_) + K2»Z.) 2 —— du- Lk3g+3¢=):3b .1 01V JAM; r§o\\oufl 0-8; +\Ac\\- M Eth C o aisle m ¥unc¥mn$ WH'K" Who}? is "M ’Q “0 \OQU‘\.\\3 7. The length of horse pregnancies from conception to birth Varies according to a roughly normal distribution with Inean 336 days and standard deviation 3 days- Use the 68-95—9937 rule to answer the following questions H 5 e I O... z 3 a- (6 pts.) All'nost all (99.7%))horfie pregnancies full in what range of lengths? 0446’) rt+3orjz= [336-—-°l ) 33¢+°l1 '7:— ) sits-3 b. (7 pts.) What percent of horse pregnancies are longer than 339 days? I: 335 —~ 3 3391—3] ->é% °/, Mal, 8. Using rI‘ahle A find the proportion of observation fronl a standard normal distribution for each of the following events- P( 7.71.51): 1— N14 1.61) :1 4* 0352.3- : 0.0Lt'15 a. (5 pts-) Z > 1.67 . P(1¢\.b1) —- ‘PL 2- 4‘1) =1- o.€\sa_s— 0.02.1?! flm 9. Find the value 2 of standard normal variable Z that satisfies each of the following conditions. (Report the value of 2: that. comes closest to satisfying the condition.) In each case, sketch :1 standard nornlal curve’yvitll your value of z :narked on the axis. 1). (6 pts.) —2 <1 Z c: 1.67 a. ([5 pts.) 20% of the observations fall below 3. FL 2 (a) 70.; => azo-SH b. (6 pts.) 30% ofthe observations fall above 2. & qOug 10. The diameter inches) at breast height of trees of certain type is normally distributed with p = 8.8 and a = 2.8 as suggested in the article Thinning” (Fmst Pmducts J., May 1997: 36-41). 3.. “Simulating a Harvester-Forwarder Sefiwuod (7 pts.) What proportion of tree diameters fall between 8.0 and 9.5 in? Pk 75.0 <. KC ‘16} : PL 2...?5 l‘g‘ a: “.0351 < 2. < 0.2.5) r: P( 240.23) —-\3( % <-o.9—°l) '= o-‘S‘ls'r -—0.%%s=1 : 0.2428 b. (8 pts.) What diameter value separates the largest 75% of all tree diameters from the others? P( X4 a): 0.2.3 > c 0. Lq \_// 1‘8 . 02.5 q ‘1" 9""? zeta“! => a: 85.8 ~CL‘%)(° h) . 2-3 . — e .fiz—Lr c. Extra credit (7 pts.) BetWeen what values do the dim—eters of the middle 75 % of all trees fall? I - If." ? {X<—-q?) = 0.113 I %<?‘—qh gig): Kill; / 2.8 _ =_ 2.3 @133 _0\ 934'5‘ Hwfi—RJS ._.) q:(?.2)_,2_ ‘ (E - m _ 11. (9 pts.) Establish the correspondence between the scatterplots below and their (real-u ranged) correlations: r z “.7, r = O, r = .5, r : __3, r m .9, r :_t.—.99 . 12. There is some evidence that drinking moderate amount of wine helps prevent heart attacks. The scatterplot below provided by MINITAB gives data on yearly wine consumption (liters of alcohol from drinking wine per person (horizontal axis”, and yearly deaths from heart disease {deaths per 100,000 population) in 19 developed nations. ' ' 7.86 R—Sq 71.0% .- R-5q(adj) __ _. a. (6 pts.) According to the above printout, r2 : .71 . What is the value of r? m: 0.8 42¢, from; Mae’r'xwa assoc—taken b. (6 pts.) Use the abovevequation of the least squares regression line to predict the value of the heart disease deaths for the value I : 3.2 liters. §:(9_60.é)-@-1-°l'l)(3-9’) = \87-0'14; 13. Consolidated Builders has bid on tWo large construction projects. The company president believes that the probability of winning the first contract (event A) is 0.6, that the probability of winning the second (event B) is 0.5, and that the probability of winning both jobs (event {AondB} is 0.3. Use standard operations to express each of the following events in terms of A , B, A“ , and B" , and find their probability. For each of the events draw the Venn diagram and shade the event in question. a. (5 pts.) Consolidated wins at least one of the jobs? A!) r g g or B): o-G+0.S “0.9) A @22 = as b. (5 pts.) Consolidated wins both jobs. A Mai ‘93 C. c. (5 pts.) Consolidated wins the first job, but not the second. A M B MAM; 93‘): mtg—swam; #5) A63?) -: 0.6 - O«3=* g C d. (5 pts.) Consolidated does not win the first job, but does win the second. 8 Andi A B P(99MAp<c)-=PKQW—PM~AB) L e. (5 pts.) Consolidated does not win either job. O f B 3 _...\ °r It- PLAor g) -_-_- l" Untraz fl °’ mtwmc). MN»; 5‘) 14. In a certain population of voters 60 % are Republicans and 40% are Democrats. It is reported that 30% of the Republicans aiid 80% of Democrats favor a certain election issue. a. (7 pts.) Find the probability that a voter chosen at random from this population favors the issue in question. éIése either the Venn diagram , or the tree diagram technique.) 9‘ 948' Rewbufm oust {now 5 *«vaf 5 0.50 ...
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