Midtermsol - GE331 / IE 300 Analytic Methods For...

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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: {gully-m 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: 2-m- 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 mfg-i542“ 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't-mU'EUJH mmte-MMI—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.:§+ gait-ms 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. One-fourth of these treatment-caused 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 (ax-aided 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 : Mummy-r PCSiM’}P(M’)m@.§xo-ooi3 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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This note was uploaded on 01/26/2012 for the course IE IE 300 taught by Professor Zafarani during the Spring '09 term at University of Illinois, Urbana Champaign.

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Midtermsol - GE331 / IE 300 Analytic Methods For...

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