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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 illyour frequency table is 50) ' I
Sm 9.; J<‘\’\C re\_ Jill, _ I 2.
gFEﬁpLencies Must Lac. 4 . €35 ~4<v\\€_ tun55.x“ «ck.
gweckumcy (S l 0.2.0 {00 Iv (3 pts.) It is kuoWn that. ifu histogram: is positively Sklchﬂl, 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.(Jimutho(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 chia (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 inlmrqumtilu range {Hell} and poinl. out. outliers, if any
(um tin IIiLa IQ“ ('l‘iiJEI'iUII) K": (3555" : (gr2 :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 08; +\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 6895—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:— ) sits3 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.; => azoSH 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: 3641). 3.. “Simulating a HarvesterForwarder 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)
. 23 . — 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 (realu 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% .
R5q(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)[email protected]°l'l)(39’)
= \870'14; 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): oG+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.)
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 Summer '08
 NANE
 Normal Distribution, Standard Deviation, pts, relative frequency histogram

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