Solution Manual for Applied Statistics and Probability for Engineers, 7th Edition

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Applied Statistics and Probability for Engineers,7thedition20172-1CHAPTER 2Section 2-1Provide a reasonable description of the sample space for each of the random experiments inExercises 2.1.1 to 2.1.11.There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.2.1.1.Each of four transmitted bits is classified as either in error or not in error.Leteandodenote a bit in error and not in error(odenotes okay), respectively.oooooeooeoooeeoooooeoeoeeooeeeoeooeooeeoeoeoeeeoooeeoeeeeoeeeeeeS,,,,,,,,,,,,,,,2.1.2.The number of hits (views) is recorded at a high-volume Web site in a day.,...2,1,0S= set of nonnegative integers2.1.3.In the final inspection of electronic powersupplies, either units pass, or three types of nonconformities might occur:functional, minor, or cosmetic. Three units are inspected.Letadenote an acceptable power supply.Letf,m,andcdenote apowersupplythat hasa functional, minor, or cosmetic error, respectively.cmfaS,,,2.1.4.An ammeter that displays three digits is used to measure current in milliamperes.A vector with three components can describe the threedigits of the ammeter. Each digit can be0,1,2,...,9.The samplespaceSis1000 possible three digit integers,999,...,001,000S2.1.5.The following two questions appear on an employee survey questionnaire. Each answer is chosen from the five pointscale 1 (never), 2, 3, 4, 5 (always).Is the corporation willing to listen to and fairly evaluatenew ideas?How often are my coworkers important in my overalljob performance?Let an ordered pair of numbers, such as 43 denote the response on the first and second question.Then, Sconsistsofthe 25 ordered pairs111255,,...,2.1.6.The time until a service transaction is requested of a computer to the nearest millisecond.,...,2,1,0Sin milliseconds2.1.7.The pH reading of a water sample to the nearest tenth of a unit.0.14,2.1,1.1,0.1S2.1.8.The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category ismeasured by an optical inspection of a sample.Lets,m, andldenote small, medium, and large, respectively. ThenS= {s,m,l,ss,sm,sl, ….}2.1.9.A sampled injection-molded part could have been produced in either one of two presses and in any one of the eight

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Applied Statistics and Probability for Engineers,7thedition20172-2cavities in each press.PRESSCAVITY1212345678123456782.1.10.An order for an automobile can specify either an automatic or a standard transmission, either with or without airconditioning, and with any one of the four colors red, blue, black, or white. Describe the set of possible orders forthisexperiment.automatictransmissiontransmissionstandardwithoutwithairwithoutairairairwithwhiteredblueblackwhiteredblueblackwhiteredblueblackwhiteredblueblack2.1.11.Calls are repeatedly placed to a busy phone line until a connection is achieved.Letcandbdenoteconnectandbusy,respectively. ThenS= {c,bc,bbc,bbbc,bbbbc, …}2.1.12.Threeattempts are made to read data in a magnetic storage device before an error recovery procedure that repositionsthe magnetic head is used. The error recovery procedure attempts three repositionings before an “abort’’ message issent to the operator. Letsdenote the success of a read operationfdenote the failure of a read operationSdenote the success of an error recovery procedureFdenote the failure of an error recovery procedureAdenote an abort message sent to the operatorDescribe the sample space of this experiment with a tree diagram.fffFFFAfffFFSfffFSfffSffsfssS,,,,,,

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Applied Statistics and Probability for Engineers,7thedition20172-32.1.13.Three events are shown on the Venn diagram in the following figure:Reproducethe figure and shade the region that corresponds toeach of the following events.(a)A(b)AB(c)ABC(d)BC(e)ABC(a)(b)(c)(d)

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Applied Statistics and Probability for Engineers,7thedition20172-4(e)2.1.14In an injection-molding operation, the length and width, denoted asXandY, respectively, of each molded part areevaluated. LetAdenote the event of 48 <X< 52 centimetersBdenote the event of 9 <Y< 11 centimetersConstruct a Venn diagram that includes these events. Shade the areas that represent the following:(a)A(b)AB(c)AB(d)AB(e) If these events were mutually exclusive, how successful would this production operation be? Would the processproduce parts withX50 centimeters andY= 10 centimeters?(a)(b)AB4852119AB4852119

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Applied Statistics and Probability for Engineers,7thedition20172-5(c)(d)(e)If the events are mutually exclusive, then AB isthe null set.Therefore, the process doesnot produceproduct partswithX=50 cm andY=10 cm. The process would not be successful.2.1.15.A digital scale that provides weights to the nearest gram is used.(a)What is the sample space for this experiment?LetAdenote the event that a weight exceeds 11 grams, letBdenote the event that a weight is less than or equal to15 grams, and letCdenote the event that a weight is greater than or equal to 8 grams and less than 12 grams.Describe the following events.(b)AB(c)AB(d)A(e)ABC(f)AC(g)ABC(h)BC(i)ABC(a)LetS=thenonnegative integers from 0 to the largest integer that can be displayed by the scale.LetXdenote theweight.Ais the event thatX> 11Bis the event thatX15Cis the event that 8X<12S= {0, 1, 2, 3, …}(b)S(c) 11 <X15 or {12, 13, 14, 15}(d)X11 or {0, 1, 2, …, 11}(e)S(f)ACcontainsthe values ofXsuch that:X8Thus (AC)containsthe values ofXsuch that:X< 8 or {0, 1, 2, …, 7}(g)(h)Bcontainsthe values ofXsuch thatX> 15. Therefore,BCisthe empty set. Theyhave no outcomes in common or.(i)BCis the event 8X <12. Therefore,A(BC) is the eventX8 or {8, 9, 10, …}2.1.16.In light-dependent photosynthesis, light quality refers to the wavelengths of light that areimportant. The wavelengthof a sample of photosynthetically active radiations (PAR) is measured to the nearest nanometer. The red range is 675–700 nm and the blue range is 450–500 nm. LetAdenote the event that PAR occurs in the red range, and letBdenotethe event that PAR occurs in the blue range. Describe the sample space and indicate each of the following events:AB4852119AB4852119

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Applied Statistics and Probability for Engineers,7thedition20172-6(a)A(b)B(c)AB(d)ABLetwdenote the wavelength.The sample space is {w| w = 0, 1, 2, …}(a)A={w|w= 675, 676, …, 700 nm}(b)B={w|w= 450, 451, …, 500 nm}(c)BA(d)BA{w|w= 450, 451, …, 500, 675, 676, …, 700 nm}2.1.17.Four bits are transmitted over a digital communications channel. Each bit is either distorted or received withoutdistortion. LetAidenote the event that theith bit is distorted,i1,,4.(a) Describe the sample space for this experiment.(b) Are theAi’s mutually exclusive?Describe the outcomes in each of the following events:(c)A1(d)A1(e)A1A2A3A4(f)A1A2A3A4Letdandodenote a distorted bit andone that is not distorted (odenotes okay), respectively.(a)ooooodoodoooddooooodododdoodddodoodooddodododddoooddoddddoddddddS,,,,,,,,,,,,,,,(b) No, for exampleddooddoddddoddddAA,,,21(c)doooddoodoodddoddododddododdddddA,,,,,1(d)ooooodooooodododoodooddoooddodddA,,,,,,,1(e)}{4321ddddAAAA(f)ddooooddddododdddddododdddddAAAA,,,,,,)()(43212.1.18.Disks ofpolycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100disks are summarized here:

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Applied Statistics and Probability for Engineers,7thedition20172-7LetAdenote the event that a disk has high shock resistance, and letBdenote the event that a disk has high scratchresistance. Determine the number of disks inAB, A,andAB.AB = 70, A= 14, AB = 952.1.19.In control replication, cells are replicated over a period of two days. Not until mitosis is completed canfreshly synthesized DNA bereplicated again. Two control mechanisms have been identified—one positive and onenegative. Suppose that a replication is observed in three cells. LetAdenote the event that all cells are identified aspositive, and letBdenote the event that all cells are negative. Describe the sample space graphically and display eachof the following events:(a)A(b)B(c)AB(d)ABLetPandNdenotepositive and negative, respectively.The sample space is {PPP,PPN,PNP,NPP,PNN,NPN,NNP,NNN}.(a)A={PPP}(b)B={NNN}(c)BA(d)BA{PPP,NNN}2.1.20.Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The resultsfrom 100 samples aresummarized as follows:LetAdenote the event that a sample is from supplier 1, and letBdenote the event that a sample conforms tospecifications. Determine the number of samples inAB, Band inAB.BA= 55,B=23,BA= 852.1.21.The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space be positive,real numbers. Define the eventsAandBas follows:Ax|x725andBx|x525.Describe each of the following events:(a)A(b)B(c)AB(d)AB(a)A= {x|x72.5}(b)B= {x|x52.5}(c)AB= {x| 52.5 <x< 72.5}

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Applied Statistics and Probability for Engineers,7thedition20172-8(d)AB= {x|x> 0}2.1.22.The following tablesummarizes 204 endothermic reactions involving sodium bicarbonate.LetAdenote the event that a reaction’s final temperature is 271 K or less. LetBdenote the event that the heat absorbedis below target. Determine the number of reactions ineach of the following events.(a)AB(b)A(c)AB(d)AB(e)AB(a)AB= 56(b)A=36 + 56 = 92(c)AB=40 + 12 + 16 + 44 + 56 = 168(d)AB= 40+12+16+44+36=148(e)AB= 362.1.23.A Web ad can bedesigned from four different colors, three font types, five font sizes, three images, and five textphrases. How many different designs are possible?Total number of possible designs =900535342.1.24.Consider the hospital emergency department data given below. LetAdenote the event that a visit is to hospital 1, andletBdenote the event that a visit results in admittance to any hospital.Determine the number of persons in each of the following events.(a)AB(b)A(c)AB(d)AB(e)AB(a)AB= 1277(b)A=22252–5292 = 16960(c)AB=1685 + 3733 + 1403 + 2 + 14 + 29 + 46 + 3 = 6915(d)AB= 195 + 270 + 246 + 242+ 3820 + 5163 + 4728 + 3103 + 1277 = 19044(e)AB= 270 + 246 + 242 + 5163 + 4728 + 3103 = 137522.1.25.The article “Term Efficacy of Ribavirin Plus Interferon Alfa in the Treatment of Chronic Hepatitis C,”[Gastroenterology(1996, Vol. 111, no. 5, pp. 1307–1312)], considered the effect of two treatments and a control fortreatment of hepatitis C. The following table provides the total patients in each group and the number that showed acomplete (positive) response after 24 weeks of treatment.

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Applied Statistics and Probability for Engineers,7thedition20172-9LetAdenote the event that the patient was treated with ribavirin plus interferon alfa, and letBdenote the event that theresponse was complete. Determine the number of patients in each of the following events.(a)A(b)AB(c)AB(d)ABLet |A| denote the number of elements in the set A.(a) |A| = 21(b) |A∩B| = 16(c) |A⋃B| = A+B-(A∩B) = 21+22–16 = 27(d) |A'∩B'| = 60-|AUB| = 60–27 = 332.1.26.A computer system usespasswords that contain exactly eight characters, and each character is 1 of the 26 lowercaseletters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Letdenote the set of all possible passwords, and letAandBdenote the events that consist of passwords with only letters or only integers, respectively. Determine the numberof passwords in each of the following events.(a)(b)A(c)AB(d) Passwords that contain at least 1 integer(e) Passwords that contain exactly 1 integerLet |A| denote the number of elements in the set A.(a) The number of passwords inis= 628(from multiplication rule).(b) The number of passwords in A is |A|= 528(from multiplication rule)(c) A' ∩ B' = (A U B)'. Also, |A| = 528and |B| = 108and A ∩ B = null. Therefore,(A U B)' =628-528-108≈1.65 x 1014(d) Passwords that contain at least 1 integer = ||-|A| = 628–528≈ 1.65 x 1014(e) Passwords that contain exactly 1 integer. The number of passwords with 7 letters is 527. Also, 1 integer is selectedin 10 ways, and can be inserted into 8 positions in the password. Therefore, the solution is 8(10)(527) ≈ 8.22 x 1013Section 2-22.2.1.A sample of two printed circuit boards isselected without replacement from a batch. Describe the (ordered)sample space for each of the following batches:(a) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 2 boards with major defects.(b) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 1 board with major defects.Letgdenote a good board,ma board with minor defects, andja board with major defects.(a)S= {gg, gm, gj, mg, mm, mj, jg, jm, jj}(b)S={gg,gm,gj,mg,mm,mj,jg,jm}2.2.2.A sample of two items is selected without replacement from a batch. Describe the (ordered) sample space for each ofthe following batches:(a) The batch contains the items {a,b,c,d}.(b) The batch contains the items {a,b,c,d,e,f,g}.(c) The batch contains 4 defective items and 20 good items.(d) The batch contains 1 defective item and 20 good items.(a) {ab, ac, ad, bc, bd, cd, ba, ca, da, cb, db, dc}

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Applied Statistics and Probability for Engineers,7thedition20172-10(b){ab, ac, ad, ae, af, ag,ba,bc, bd, be, bf, bg,ca,cb,cd, ce, cf, cg,da,db,dc,de, df, dg,ea,eb,ec,ed,ef,eg,fa,fb,fc,fg,fd,fe,ga, gb, gc, gd, ge, gf},contains42elements(c) Letdandgdenotedefectiveandgood, respectively. ThenS= {gg, gd, dg, dd}(d) S = {gd, dg, gg}2.2.3.A wireless garage door opener has a code determined by the up or down setting of 12 switches. How manyoutcomes are in the sample space of possible codes?212= 40962.2.4.In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machinetools, four polishing tools, and three painting tools, how many different routings (consisting of machining, followed bypolishing, and followed by painting) for a part are possible?From the multiplication rule,343362.2.5.New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locationsfor input valves, and four locations for output valves. How many different productdesigns are possible?From the multiplication rule,34341442.2.6.A manufacturing process consists of 10 operations that can be completed in any order. How many different productionsequences are possible?From equation 2.1, the answer is 10! = 3,628,8002.2.7.A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do notconform to customer requirements.(a) How many different samples are possible?(b) How many samples of five contain exactly one nonconforming chip?(c) How many samples of five contain at least one nonconforming chip?(a) From equation 2-4, the number of samples of size five is528,965,416!135!5!1401405(b) There are 10 ways of selecting one nonconforming chip and there are880,358,11!126!4!1301304ways of selecting four conforming chips. Therefore, the number of samples that contain exactly onenonconforming chip is 10800,588,1131304(c) The number of samples that contain at least one nonconforming chip is the total number of samples5140minus the number of samples that contain no nonconforming chips5130. That is5140-5130=752,721,130!125!5!130!135!5!1402.2.8.In a sheet metal operation, three notches and four bends are required. If the operations can be done in any order,how many different ways of completing the manufacturing arepossible?From equation 2-3,73 435!!!sequences are possible2.2.9.In the laboratory analysis of samples from a chemical process, five samples from the process are analyzed daily. Inaddition, a control sample is analyzed twice each day to check the calibration of the laboratory instruments.(a) How many different sequences of process and control samples are possible each day? Assume that the five processsamples are considered identical and that the two control samples are considered identical.

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Applied Statistics and Probability for Engineers,7thedition20172-11(b) How many different sequences of process and control samples are possible if we consider the five process samplesto be different and the two control samples to be identical?(c) For the same situation as part (b), how manysequences are possible if the first test of each day must be a controlsample?(a)21!5!2!7sequences are possible.(b)2520!2!1!1!1!1!1!7sequences are possible.(c) 6! = 720 sequences are possible.2.2.10.In the layout of aprinted circuit board for an electronic product, 12 different locations can accommodate chips.(a) If five different types of chips are to be placed on the board, how many different layouts are possible?(b) If the five chips that are placed on the board are of the same type, how many different layouts are possible?(a) If the chips are of different types, then every arrangement of 5 locations selected from the 12 results in adifferent layout. Therefore,040,95!7!12125Playouts are possible.(b) If the chips are of the same type, then every subset of 5 locations chosen from the 12 results in a differentlayout. Therefore,792!7!5!12125layouts are possible.2.2.11.Consider the design of acommunication system.(a) How many three-digit phone prefixes that are used to represent a particular geographic area (such as an area code)can be created from the digits 0 through 9?(b) As in part (a), how many three-digit phone prefixes are possible that do not start with 0 or 1, but contain 0 or 1 asthe middle digit?(c) How many three-digit phone prefixes are possible in which no digit appears more than once in each prefix?(a) From the multiplication rule, 1031000prefixes are possible(b) From the multiplication rule,8210160are possible(c) Every arrangement of three digits selected from the 10 digits results in a possible prefix.P310107720!!prefixes are possible.2.2.12.In the design of an electromechanical product, 12 components are to be stacked into a cylindrical casing in a mannerthat minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top.(a) If all components are different, how many different designs are possible?(b) If seven components are identical to one another, but the others are different, how many different designs arepossible?(c) If three components are of one type and identical to one another, and four components are of another type andidentical to one another, but the others are different, how many different designs are possible?(a) Every arrangement selected from the 12different componentscomprisesa different design.Therefore,600,001,479!12designs are possible.(b) 7components are the same, others are different,95040!1!1!1!1!1!7!12designs are possible.(c)3326400!4!3!12designs are possible.

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Applied Statistics and Probability for Engineers,7thedition20172-122.2.13.A bin of 50 parts contains 5 that are defective. A sample of 10 parts is selected atrandom, without replacement. Howmany samples contain at least four defective parts?From the 5 defective parts, select 4, and the number of ways to complete this step is 5!/(4!1!) = 5From the 45 non-defective parts, select 6, and the number of ways to complete this step is 45!/(6!39!) = 8,145,060Therefore, the number of samples that contain exactly 4 defective parts is 5(8,145,060) = 40,725,300Similarly, from the 5 defective parts, the number of ways to select 5 is 5!(5!1!) = 1From the 45 non-defective parts, select 5, and the number of ways to complete this step is 45!/(5!40!) = 1,221,759Therefore, the number of samples that contain exactly 5 defective parts is1(1,221,759) = 1,221,759Therefore, the number of samples that contain at least 4 defective parts is40,725,300 + 1,221,759 = 41,947,0592.2.14.Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Eachtool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. Aninspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction thatresults in parts that donot conform to specifications.(a) How many samples contain exactly 1 nonconforming part?(b) How many samples contain at least 1 nonconforming part?(a) The total number of samples is312123 9220!!!.The number of samples that result in onenonconforming part is .90!8!2!10!1!1!210221Therefore, the requested probability is90/220 = 0.409.(b) The number of samples with no nonconforming part is.120!7!3!10103The probability of at least onenonconforming part is 1455.0220120.2.2.15.A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day.Supposethat an operating room needs to handle three knee, four hip, and five shoulder surgeries.(a) How many different sequences are possible?(b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?(c) How many different schedules begin and end with a knee surgery?(a) From the formula for the number of sequences12!3!4!ହ!= 27,720 sequences are possible.(b) Combining all hip surgeries into one single unit, all knee surgeries into one single unit and all shoulder surgeriesinto one unit, the possible number of sequences of these units = 3! = 6(c)With two surgeries specified, 10 remain and there are10!4!ହ!1!= 1,260 different sequences.Section 2-32.3.1.The sample space of a random experiment is {a,b,c,d,e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2, respectively.LetAdenote the event {a,b,c}, and letBdenote the event {c,d,e}. Determine the following:(a)P(A)(b)P(B)(c)P(A')(d)P(AB)(e)P(AB)(a) P(A) = 0.4(b) P(B) = 0.8(c) P(A') = 0.6(d) P(AB) = 1

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Applied Statistics and Probability for Engineers,7thedition20172-13(e) P(AB) = 0.22.3.2.A part selected for testing is equally likely to havebeen produced on any one of six cutting tools.(a) What is the sample space?(b) What is the probability that the part is from tool 1?(c) What is the probability that the part is from tool 3 or tool 5?(d) What is the probability that the part is not from tool 4?(a) S = {1, 2, 3, 4, 5, 6}(b) 1/6(c) 2/6(d) 5/62.3.3.An injection-molded part is equally likely to be obtained from any one of the eight cavities on a mold.(a) What is the sample space?(b) What is the probability that a part isfrom cavity 1 or 2?(c) What is the probability that a part is from neither cavity 3 nor 4?(a) S = {1,2,3,4,5,6,7,8}(b) 2/8(c) 6/82.3.4.A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If anumber is enteredrandomly, what is the probability that it is a valid number?Total possible: 1016,but only 108arevalid. Therefore,P(valid) = 108/1016= 1/1082.3.5.In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multipleoxidation states and that is usually found in the following states:(a) What is the probability that a cell has at least one of the positive nickel-charged options?(b) What is the probability that a cell isnotcomposed of a positive nickel charge greater than +3?The sample space is {0, +2, +3, and +4}.(a)The event that a cell has at least one of the positive nickel charged options is {+2, +3, and +4}. The probability is0.35+0.33+0.15= 0.83.(b)The event that a cell is not composed of a positive nickel charge greater than +3 is {0, +2, and +3}. Theprobability is 0.17+0.35+0.33= 0.85.2.3.6.A message can follow different paths through servers on a network. The sender’s message can go to one of five serversfor the first step; each of them can send to five servers at the second step; each of those can send to four servers at thethird step; and then the message goes to the recipient’s server.(a) How many paths are possible?(b) If all paths are equally likely, what is the probability that a message passes through the first of four servers at thethird step?(a) 5*5*4 = 100(b) (5*5)/100 = 25/100=1/4

Solution Manual for Applied Statistics and Probability for Engineers, 7th Edition - Page 15 preview image

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Applied Statistics and Probability for Engineers,7thedition20172-142.3.7.Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0 and9) followed by three letters (betweenAandZ). If a license number is selected randomly, what is the probability thatyours is the one selected?3 digits between 0 and 9, so the probability of any threenumbers is 1/(10*10*10).3 letters A to Z, so the probability of any three numbers is 1/(26*26*26).The probability your license plateis chosen is then (1/103)*(1/263) = 5.7 x 10-82.3.8.Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100disks are summarized as follows:LetAdenote the event that a disk has high shock resistance, and letBdenote the event that a disk has high scratchresistance. If a disk is selected at random, determine the following probabilities:(a)P(A)(b)P(B)(c)P(A')(d)P(AB)(e)P(AB)(f)P(A’B)(a) P(A) = 86/100 = 0.86(b) P(B) = 79/100 = 0.79(c) P(A') = 14/100 = 0.14(d) P(AB) = 70/100 = 0.70(e) P(AB) =(70+9+16)/100 = 0.95(f) P(A’B) = (70+9+5)/100 = 0.842.3.9.Magnesium alkyls are used as homogenous catalysts in the production of linear low-density polyethylene (LLDPE),which requires a finer magnesium powder to sustain a reaction. Redoxreaction experiments using four differentamounts of magnesium powder are performed. Each result may or may not be further reduced in a second step usingthree different magnesium powder amounts. Each of these results may or may not be further reduced in athird stepusing three different amounts of magnesium powder.(a) How many experiments are possible?(b) If all outcomes are equally likely, what is the probability that the best result is obtained from an experiment thatuses all three steps?(c) Does the result in part (b) change if five or six or seven different amounts are used in the first step? Explain.(a)The number of possibleexperiments is4 + 4 × 3 + 4 × 3 × 3 = 52(b) There are 36 experiments that use all three steps. The probability the best result uses all three steps is 36/52 =0.6923.(c)No, it will not change.Withkamounts in the first step the number of experiments isk+ 3k+ 9k= 13k.The number of experiments that complete all three steps is 9kout of 13k. Theprobability is 9/13 = 0.6923.2.3.10.An article in theJournal of Database Management[“Experimental Study of a Self-Tuning Algorithm for DBMSBuffer Pools” (2005, Vol. 16, pp. 1–20)] provided the workload used in the TPC-C OLTP (Transaction ProcessingPerformance Council’s Version C On-Line Transaction Processing) benchmark, which simulates a typical order entryapplication.

Solution Manual for Applied Statistics and Probability for Engineers, 7th Edition - Page 16 preview image

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Applied Statistics and Probability for Engineers,7thedition20172-15The frequency of each type of transaction (in the second column) can be used as the percentage of each type oftransaction. The average number ofselectsoperations required for each type of transaction is shown. LetAdenote theevent of transactions with an average number ofselectsoperations of 12 or fewer. LetBdenote the event oftransactions with an average number ofupdatesoperations of 12 or fewer. Calculate the following probabilities.(a)P(A)(b)P(B)(c)P(AB)(d)P(AB’)(f)P(AB)(a) The total number of transactions is 43+44+4+5+4=10052.01004444)(AP(b)95.01005100)(BP(c)52.01004444)(BAP(d)0)'(BAP(e)95.01005100)(BAP2.3.11.Samples of emissions from three suppliers areclassified for conformance to air-quality specifications. The results from100 samples are summarized as follows:LetAdenote the event that a sample is from supplier 1, and letBdenote the event that a sample conforms tospecifications. If a sample is selected at random, determine the following probabilities:(a)P(A)(b)P(B)(c)P(A')(d)P(AB)(e)P(AB)(f)P(A’B)(a) P(A) = 30/100 = 0.30(b) P(B) = 77/100 = 0.77(c) P(A') = 1–0.30 = 0.70(d) P(AB) = 22/100 = 0.22(e)P(AB) = 85/100 = 0.85(f) P(A’B) =92/100 = 0.922.3.12.Consider the hospital emergency room data is given below. LetAdenote the event that a visit is to hospital 4, and letBdenote the event that a visit results in LWBS (at anyhospital).

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