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Unformatted text preview: GE331 / IE 300 Analytic Methods For Uncertainty / Analysis of Data Spring 2011 University of Illinois G. Koksal PART 1: 7:00 — 7:45 pm
PART 2: 7:50 — 8:30 pm Open textbook, lecture notes and/0r cheat sheets and 2 table.
Calculators are allowed. NAME: {gullym K? 5 Please clearly PRINT your name in CAPITAL LETTERS. PART 1 (54 points) PART II (1.? points) 1 (6 points) 2 (10 points) 3 (15 points) 4 (12 points) I 5 (4 points) Total (ﬁspoints) 24.02.2011 GE331/IE300
EXAM 1
PART I (54 points) Duration: 45 minutes 1) Which of the following variables use the ratio scale of measurement?
a) Citizenship number
b) temperature in come 2) Five hundred residents of Chicago are polled to obtain information on voting intentions in an upcoming city
election. The ﬁve hundred residents in this study is an example of a(n) census , sample observation population 3) The following is a box plot of glucose level of 180 individuals. Which one of the following statements is
correct? 1
The distribution is positively skewed (longer tail at right)
"i The mean and the median are the same
0) The ﬁrst quartile is less than 75. '
d) The median is around 100.
e) The upper whisker extends only to the largest point in the data. 225 200 175 150 125 ﬂucoselevel IOU 7S 4) A new soft drink is being market tested. It is estimated that 85% of consumers will like the new drink. A
sample of 68 consrimers tested the new drink. What is the probability that less than 75% of the consumers will
indicate they like the drink? (Use a normal approximation with a correction factor to find the probability.) "'. 001044
0) 0.01618 d) 0.01801 5) Service times at a fast food restaurant are distributed with a mean of 5 minutes and variance of 0.5 minutes? Which of the following is the closest approximation for the probability that the difference between the total
service time of 100 customers and the mean total service time is within two standard deviations of the total service times? at, a) 68% ‘Tm : K;
b) 75% “it; c) 95% _. _ .... i .. 6) The number of electrical outages in a city varies from day to day. Assume that the number of electrical
outages (x) in the city has the following probability distribution. 1 a
:1: f(x) 9%“ (e.2e)ib.2)+ (twe.2e)3’(v.55’) «i (2~a2é) (see)?
0 0'80 +{swe.eg}2(e.ei) 2;: essay
1 0.15 ‘ 2 0.04 W a a.es+€2¥e.a¢r)+ €3)(e.ai)— 0.
3 0‘01 CV2: exp a mums: 2m The coefﬁcient of variation for the number of electrical outages (respectively) is
a) 0.78
Q) 2.22
c) 0.45
d) 1.28 7) The expected value of a discrete random variable X
a) is the most likely or highest probability value for the random variable
. .' . l. .a s. beoneof the val esX cantake on althou h. it ma .not be thehi hest rohabili .
random variable
is the average value for the random variable over (inﬁnitely) many repeats of the experiment
d) None of these alternatives is correct. ...va1ue for. the . . .. 8) The police records of a metropolitan area kept over the past 300 days show the following number of fatal
accidents. Number of Fatal
Accidents Number of Days mfgi542“ 0 45 9. i3“
1 75 O . ZS“
2 120 o . $9
3 45 °
4 15 : .
What is the probability that in a given day there will be less than 3 accidents?
a) 0.2
b) 120 __ 0.5
' 0.8 9) A retailer of electronic equipment received six VCRs from the manufacturer. 'Ihree of the VCRs were
damaged in the shipment. The retailer sold two VCRs to two customers (i.e. each customer purchased one
VCR). The probability that both customers reccived damaged VCRs is desired to be computed. a) A binomial formula can be used for the solution of the above problem. g X 3? The above satisﬁes hypergeometric probability distribution. 9&2} .5 __ H r __ E 3’; gﬁ c) The probability that both customers received damaged VCRs is 0.23 " i“ d) The probability that both customers received damaged VCRs is 0.30 10) The normal probability plot of the measured substance levels at the urban locations is given below. What can
you say about the distribution of substance levels at the urban locations? ML Estimates
Mean 39.0667
SlDev 39,5600 ~50 D 50 100
Data a) The substance levels can be accepted to be normally distributed. 11) The time it takes to completely tune an engine of an automobile follows an exponential distribution. The
probability of tuning an engine in less than 30 minutes 0.5276. If a tuning operation has not been ﬁnished in
30 minutes, what is the probability that it will be ﬁnished in an hour since the start of the operation? a) 0.0250 n 32:22 P MD M o) > OS) 0.7769 Mgmoraﬂeﬁ a? Wﬁnmﬁai disin'bu‘it‘or} 12) If P(A) = 0.50, P(B) = 0.60, and P(A n B) = 0.30, then events A and B are
a) mutually exclusive events
b) not independent events Q independent events
) not enough information is given to answer this question Warns“) a: Waters} as Mrs minglefedme
p.30 :2 {es/NM) 24.02.2011 GE331/IE300
EXAM 1
PART II (48 points) Duration: 40 minutes 1) (6 pts) Reconstruct the original data from the following stem—and—leaf plot: I—iwu'tmU'EUJH
mmteMMI—IQ Origina‘datm 0.9% at} a. e . l! , a. 2.5, ms, 0.3G)Q.QZ,@.S¥)Q.§EI&£0 2) (10 pts) The following table shows part of the probability distribution for a random variable X. {(x)
0.2
I? x
0
1 .
3 9 4 0.15 The mean of the above distribution is known to be 1.8 (i.e., E(X) : 1.8). Determine f(l) and f(3).
Show your work. MM: $523+ €23€M§§+ 3§(3>+(£+)(e.ts)xt.g
anest New" o.:§+ gaitms m. to ﬁ €61):Q.3
€52) : M. 3) (15 pts) A study of 31,000 hospital admissions in New York State found that 4% of the
admissions led to treatment—caused injuries. Onefourth of these treatmentcaused injuries were
caused by negligence. Malpractice claims were ﬁled in one out of 7.5 cases involving negligence
(no malpractice claims were ﬁled for other cases oftreatment—caused injury than the ones
involving negligence), and payments were made in one out of every two claims. a) What is the probability a person admitted to the hospital will suffer a treatment wcaused
injury due to negligence? .1 : ‘i‘reaimenim (axaided 333%
N :z caused bg Maia" ea. so. P(injury caused by negligence)= @ ‘ G i b) What is the probability that a malpractice claim will be ﬁled for a person admitted to the
hospital? M :: Mmifraaiw’m ﬁlm‘m ’ .._ x . £4— 0 Qaq
FEM): arms) Pm§+srmw§pmjugt§ me x :1. 3.09133? P(malpractice claim ﬁled)= a I 0 a i c) What is the probability that a malpractice claim will be paid for a person admitted to the
hospital? 8‘: Posammﬁ Meek sin. (Liam ' W
HQ : Mummyr PCSiM’}P(M’)[email protected]§xoooi3 mamas? 1:: obese? P(payment made in claim): 0 9 $9 95‘? t t a 4) (12 pts) A bank received 480 reports of lost or stolen credit cards in two years. Assume that the
number of credit card holders reporting loss or theﬁ of their credit cards each month follows a
Poisson distribution. Find approximately at least how many card holders will be reporting loss or
theft next month with probability 5%? M xsmmw {Amﬁmmrﬁﬁrﬁﬁm& Minimum number of card holders satisfying the probability c0nditi0n= — ........... _......g.........i . ..... u... . u . . u _ . . . . . . . u . uw...........r.,............... ...... a........................w..........»......a ..... u: .... u... T eof the distribution Number of tornadoes occurring in a
certain city in a seciﬁed time interval
Number of female puppies in a litter of
size 5. (Assume that a birth is equally
likely to result in a male or female pup
Number of consumers that must be
sampled until the ﬁrst environmentalist is
found ...
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 Spring '09
 Zafarani
 Normal Distribution, ........., University of Illinois G. Koksal

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