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**Unformatted text preview: **EXAM #1 Name — w i "V #' "-' '
STAT 251 Fall Quarter, 1997 Section # Li Ms. Heather Smith **ttttttt**itttitttit!tt*itttttit*****#***Itlttttt¢t**I*It****¥*#itt************t*#i**l*t$ltt**t*¢ This exam is worth 175 points. It is a closed book/closed notes exam. It has two parts (I and II). Part I: 8 multiple-choice and true/false questions; no partial credit; worth a total of 56 points. (7 points each)
Part II: 4 partial-credit questions; worth a total of 119 points. . For part I, no work is required, just identify the correct answer. / \ Ll; For part II, perform your work on the exam itself in the space provi / There is a formula sheet on the back page of the exam. ***$*********$**********¥$****l¥¥¥t¥$**¥IiiIti$$$iiititt$$¥tt¥tit$¥t¥tttttit*ttt*#*********¥¥*¥l¥¥ Part I: 1. Identify the following statement as true or false. “ ‘The number of other planets in the universe that may be
able to sustain life’ is an example of a continuous random variable." /a) True C bifFalse > 2. Tchebysheﬁ‘s Rule is important because it: @zxplains an unusual mathematical phmomenon.
shows us the difference between a skewed and a symmetric distribution. bles us to give meaning to the standard deviation.
proves that almost all of Our data values are within one standard deviation of themean. 4) explains the difference betweai the mean, the median, and the trimmed mean. you obtain at least one “tail” is (1271128).” w<‘ if 1'.-
I4" "11‘
T s
f 1)) False 4. A professor is interested in determining the average number of hours Cal Poly students sl - .
variable should the professor measure on each student she samples? Is this variable discrete continuous?
a) population mean number of hours a student slept last nigit;‘discrete“” population mean number of hours a student slept last night; continuous average number of hours a student slept last night; continuous number of hours a student slept last night; continuous
e average number of hours a student slept last night; discrete- EXAM# l: STATZSI; FallQuarterl997 (1 .._\\—Wm I
’ a 5. Identify the following statement as true or false. “For a right-skewed distribution, the mean is bigger than the
median.” b) False 6. Identify the following statement as true or false. “If two events are independent, then they are also mutually
exclgixeﬁ; @) I 0 False 7. While attending college you also work 30 hours a week managing a music store. You have just received a
shipment cm“ from Won company. You discover that m some of the compact
discs there are scratches. Suppose you wanted to quantify and then analyze the occurrence of these scratches.
Assuming that the scratches on a CD are independmt from scratch to soratch and that the occurraice of scratches
from CD to CD is indepmdent, a reasonable analysis would involve: a) Measuring the number of scratches on each sampled CD and using the binomial distribution to proceed with the analysis.
/ tiring the number of scratches on each sampled CD and using the poisson distribution to proceed
' the analysis.
c) Determining whether or not each sampled CD is scratched and using the poisson distribution to proceed
with the analysis.
d) Determining whether or not each sampled CD is scratched and using theWc distribution to proceed
with the analysis. e) Determining the total number of scratches on all 10,000 CD5, so there is no need to use distributions to analyze
our results. 8. Identify the following statement as true or false. “If we sample 2,000 values from a population, then we
/ expect at least 1,500 of them to lie within two standard deviations of the mean." a) True b) False nap..- ‘
2m -79. l —_———————————_*____;_E _\ EXAM# 1; STATZSI', FallQuarter I99?
,1.» Part II: TO RECEIVE FULL CREDIT MAKE S RE THAT YOU HOW ALL YOUR WORK AND THAT YOU ARE QOMPLETE IN YOUR ANSWERS 1. Critics of the Financial Accounting Standards Board (F A83) and the accounting profession demand a system
of accounting that is as useful to govemmmt policy makers and consumer groups as it is to investors and
creditors. To examine the importance of this issue among members of Congress, suppose that an___FASB ofﬁcial
randomly selected; members among the_2i_ members of his state’s ccmgressicnal delegation for a panel discussion of the proper role of the FASB. Unknown to the oﬂicial, 5 of me members of the ZO-member messional delegation are W What is the chance that the panel discussion at
least one Erson who is a critic of current FASB policy? (20 points) we: SW2 ctr-Mics _
S Merl-04" "ram-5 chine-S . \§
pews-Dirt“) ﬁx? ) I)(HS§)_._H 4°) INC 3: 2. Suppose that the mean and standard deviation of the annual starting salaries of recent Cal Poly graduates are
$35,000 and $1,500 respectively; also, assume that the shape of the distribution of starting salaries is mound- shaped. gr " 90/,
65de 't bah or eat/0&9 , ' ‘ 251
1- Whatpercmase of startingsalaries are inexcessof$38,000? (20 points) A , r a
{maid RU‘C 3737,15, (’8‘; 32“}?- m ._ intent-1. g.
x .1 23 $6,000 Y+2c= W57-
seooomg'h ‘57.;ou'l5idﬁp MW ( "xx
"? b. If you randomly selectzteggecent graduates, what is the probability that none of them will have a starting
salary in excess of $38,000?;:'[Assume that starting salaries are independent ﬁom graduate to graduate]
(20 points) , "his: 58,000 cm- EXAM# l: STAT 251', FallQuarter 1997 \hﬂ. "‘ 3. Suppose that the California State Insurance Commission claims that 30 percent of California drivers drive cars
that are not covered by liability, medical, or collision inSuranoe. A San Luis Obispo police ofﬁcer decides to
investigate if this percartage holds in San Luis Obispo. He stops 25 randomly selected cars driving in SLO and
detennines for each driver if the vehicle he/she is driving is cove y_insuranoe. :1. Compute the probability that at least twenty of the drivers are driving vehicles that gr; covered by inSurance.
[Assume that holding insurance is independent from car to car] (19 points) PURE :1 l ,- pus-M): I, ‘ :N. > qsmhkmw M10 oi Q
mpdit’iving W130 rcd Vt,h\d-cg_. b. How many of the cars does the police ofﬁcer expect to have insurance? (10 points) 0.]. 0‘) M
.70.], OF 26 : llgoﬂg ; 1%475 iﬁugéngw twof’ﬁcw
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9 m M msch '
Wuul , 90W I _
we” - ‘3 0? 1g cars
WDUUE \hSUKd .
4. If you pay me one dollar, I will let you play the following gambling game. You drop your pencil point into the middle of a table of random digits (integer values from 0 through 9) and than look at the digit on which it
lands. Ifthe digit is a “0”, you win $5. Ifthe digit is a “1", you win $2. Otherwise, you win nothing. it. Find the probability distribution of your overall winnings. [Hint let x = your overall winnings] (20 poin .)
_L. okwcc ac wmmvws tgﬁ‘gmtrﬁ‘; i/m wm— how much H avast? Hm- WW3 lo - n3" l
2 \ . .i )(s S s
7‘; CW“: 09 turban/‘3‘ .yez-t ﬂ- 1 G. ' ‘ g .35 aka-chee- host’s aka-Ha-“ :X ¥t gr“? 9 ‘
A0 « 24d“
\‘ h h v i
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Pix In) /|0 /w J 0"?“ /"b‘.” came yeti} espectednovernll winnings when playing this game. (10 points)
to Maw mac. o-£- wi std Yen/L c‘SbQ/thiElng}
1° WNW Gm” 0" u" ' *l 1'}. 8) +1.39% 1n -
go‘ greed We: '9 legwﬂ l ,..... \
Us: C3 in BEUEL ‘\ @“56 ./' H 'erl b-l t'l til lit-.It-‘ ta] $4 EM, Ld'x_3)+(lY.§+(¢Bgvh= —_g° @ 1 WW} WWW—lashed 4/. . e " , @ n I 2
IthJVQ-®_>Z:({LZ=J—xu)) 5: (LEZIbQ’TOJ h h VaJUR—s are. wia-hin 124:. ks . © ’P(A“)= I“ PM) @ P(AuB)=P(A)+P(B)—P(An5) © ﬂ 5 CV: —-—3<_:—-— 1507) AHmsi (1.. waned}. a": 196mg): ("Pg/EB) @ 3:: Aanatﬁare. {ILCJMSIVeJ-HW (PC/MB): @ I-F A” and b and. ﬁnale: and VIM, "{5ch
l‘ndifwdud: 9 -Hnen
'PC A n 53 ‘ P6359 P03) @ ?(An5)= _P(A]B)P(B)
61,150 ‘PCA\6)= -.— WSW P64)
aJso P<6W= 19(5)- < ) Eng—11:7 and Wu vet-54,] W—_——
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