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applied statistics and multivariate

Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions

Consider the well failure data in Exercise 2-53.Suppose that two failed wells are selected randomly (without replacement) for a follow-up review. (a) What is the probability that both are from the gneiss geo- logical formation group? (b) What is the probability that both are from the same geo-
Consider the well failure data in Exercise 1-53.Let 4 denote the event that the geological formation has more than 1000 wells and let B denote the event that a well failed. Determine the following probabilities. (a) PAB) (b) P(AUB) (c) P(AUB) (d) Use the total probability rule to determine P(4)
Consider the hospital emergency room data in Example 2-8.Suppose that three visits that resulted in LWBS are selected randomly (without replacement) for a follow-up interview. (a) What is the probability that all three are selected from Hospital 27 (b) What is the probability that all three are
Consider the hospital emergency room data in Example 2-8.Let 4 denote the event that a visit is to Hospital 4 and let B denote the event that a visit results in LWBS (at any hospital). Determine the following probabilities. (a) P(B) (b) P(AUB) (b) PAUB) (c) P4UB) (d) Use the total probability rule
Consider the endothermic reactions in Exercise 2-50.Let 4 denote the event that a reaction final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Determine the following probabilities. (a) P(B) (c) PUB) (d) Use the total probability rule to determine P(A)
An article in the British Medical Journal ["Com- parison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extracorporeal Shock Wave Lithotripsy" (1986, Vol. 82, pp. 879-892)] provided the following discussion of success rates in kidney stone re- movals. Open
Heart failures are due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances (73%) or foreign objects (27%). Natural occurrences are caused by arterial blockage (56%), disease (27%), and infection (e.g., staph infection) (17%). (a) Determine
In the 2004 presidential election, exit polls from the critical state of Ohio provided the following results: total no college degree (62%) college graduate (38%) Bush, 2004 Kerry, 2004 50% 53% 50% 46% What is the probability a randomly selected respondent voted for Bush?
The edge roughness of slit paper products increases as knife blades wear. Only 1% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 5% of products slit with worn blades exhibit roughness. If 25% of the blades in
Suppose that P(A|B) 0.2, P(A|B)=0.3, and P(B) = 0.8.What is PLAY?
Suppose that P(A|B)=0.4 and P(B) = 0.5.Determine the following: (a) P(AB) (b) P(A)
An article in the The Canadian Entomologist (Harcourt et al, 1977. Vol. 109, pp. 1521-1534) studied the life of the alfalfa weevil from eggs to adulthood. The following table shows the number of larvae that survived at each stage of development from eggs to adults. Early Late Pre- Late Eggs Larvae
Consider the well failure data in Exercise 2-53.(a) What is the probability of a failure given there are more than 1000 wells in a geological formation? (b) What is the probability of a failure given there are fewer than 500 wells in a geological formation?
Consider the hospital emergency room data in Example 2-8.Let 4 denote the event that a visit is to Hospital 4 and let & denote the event that a visit results in LWBS (at any hospital). Determine the following probabilities. (2) P(A|B) (c) P(A|B) (b) P(A|B) (d) P(BA)
Consider the endothermic reactions in Exercise 2-50.Let 4 denote the event that a reaction final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Determine the following probabilities. (a) P(A|B) (c) P(A|B) (b) P(A|B) (d) P(BA)
Suppose A and B are mutually exclusive events. Construct a Venn diagram that contains the three events A, B, and C such that P(c) 1 and P(BIC) 0.
If P(A|B) = 1, must 4 = B? Draw a Venn diagram to explain your answer.
A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters(a-2) or 10 integers (0-9). You maintain a password for this computer system. Let 4 denote the subset of passwords that begin with a vowel (eithera, e, i, o, or u) and let & denote the
A batch of 350 samples of rejuvenated mitochondria contains eight that are mutated (or defective). Two are selected, at random, without replacement from the batch. (a) What is the probability that the second one selected is de- fective given that the first one was defective? (b) What is the
A batch of 500 containers for frozen orange juice con tains five that are defective. Two are selected, at random, with- out replacement from the batch. (a) What is the probability that the second one selected is defective given that the first one was defective? (b) What is the probability that both
A lot of 100 semiconductor chips contains 20 that are defective. Two are selected randomly, without replacement, from the lot. (a) What is the probability that the first one selected is defective? (b) What is the probability that the second one selected is defective given that the first one was
A maintenance firm has gathered the following infor- mation regarding the failure mechanisms for air conditioning system evidence of gas leaks evidence of electrical failure yes no yes 55 17 32 31 The units without evidence of gas leaks or electrical failure showed other types of failure. If this
The following table summarizes the number of de- ceased beetles under autolysis (the destruction of a cell after its death by the action of its own enzymes) and putrefaction (decomposition of organic matter, especially protein, by microorganisms, resulting in production of foul-smelling matter):
Consider the data on wafer contamination and loca- tion in the sputtering tool shown in Table 2-2.Assume that one wafer is selected at random from this set. Let A denote the event that a wafer contains four or more particles, and let 8 de- note the event that a wafer is from the center of the
The following table summarizes the analysis of samples of galvanized steel for coating weight and surface roughness surface roughness coating weight high low high kow 12 16 88 34 (a) If the coating weight of a sample is high, what is the prob- ability that the surface roughness is high? (b) If the
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and length measure- ments. The results of 100 parts are summarized as follows: length excellent good surface finish excellent 80 good 10 Let A denote the event that a sample has excellent surface finish,
The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed: total textural transformation yes total color transformation yes 243 13 no 26 18 (a) If a leaf completes the color transformation, what is the probability
Samples of skin experiencing desquamation are ana- lyzed for both moisture and melanin content. The results from 100 skin samples are as follows: melanin content high low moisture high 13 7 content 48 32 Let A denote the event that a sample has low melanin content, and let B denote the event that a
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: scratch resistance shock resistance high low high 70 9 low 16 5 Let A denote the event that a disk has high shock resistance. and let B denote the
Consider the well failure data in Exercise 2-53.Let A denote the event that the geological formation has more than 1000 wells and let B denote the event that a well failed. Use the addition rules to calculate the following probabilities. (a) P(AUB) (b) PAUB) (c) PA" U B')
Consider the hospital emergency room data in Example 2-8.Let A denote the event that a visit is to Hospital 4 and let B denote the event that a visit results in LWBS (at any hospital). Use the addition rules to calculate the following probabilities. (a) P(AUB) (b) P(AUB) (c) P(A'U B')
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red and let 8 denote the event that the
Consider the endothermic reactions in Exercise 2-50.Let A denote the event that a reaction final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Use the addition rules to calculate the following probabilities. (a) P(AUB) (c) P(AUB) (b) P(AUB)
A computer system uses passwords that are six char- acters and each character is one of the 26 letters (a-z) or 10 in- tegers (0-9). Uppercase letters are not used. Let 4 denote the event that a password begins with a vowel (eithera, e, i, o, or u) and let 8 denote the event that a password ends
A manufacturer of front lights for automobiles tests lamps under a high-humidity; high-temperature environment using intensity and useful life as the responses of interest. The following table shows the performance of 130 lamps: useful life satisfactory unsatisfactory intensity satisfactory
Cooking oil is produced in two main varieties: mono- and polyunsaturated. Two common sources of cooking oil are corn and canola. The following table shows the number of bottles of these oils at a supermarket: type of unsaturation type of oil canola corn mono 7 13 poly 93 77 (a) If a bottle of oil
The analysis of shafts for a compressor is summarized by conformance to specifications. roundness conforms yes surface finish conforms yes 345 5 12 (a) If a shaft is selected at random, what is the probability that the shaft conforms to surface finish requirements? (b) What is the probability that
Strands of copper wire from a manufacturer are ana- lyzed for strength and conductivity. The results from 100 strands are as follows: strength high low high conductivity 74 8 low conductivity 15 3 (a) If a strand is randomly selected, what is the probability that its conductivity is high and its
Disks of polycarbonate plastic from a supplier are an- alyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: scratch resistance shock resistance high low high 70 9 low 16 (a) If a disk is selected at random, what is the probability that its scratch
In the article "ACL Reconstruction Using Bone- Patellar Tendon-Bone Press-Fit Fixation: 10-Year Clinical Results" in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13.pp. 248-255), the following causes for knee injuries were considered: Activity Contact sport Noncontact sport Activity
If A, B, and C are mutually exclusive events with P(A) = 0.2, P(B) = 0.3, and P(C)= 0.4, determine the fol- lowing probabilities: (a) PAUBUC) (c) PAB) (e) PAnne) (b) PANC) (d) P(B)
If P(4) 0.3.P(B) = 0.2, and P(B) = 0.1.determine the following probabilities: (a) P(A') (d) P(AB) (b) P(AUB) (e) P(AUB)] (c) PAB) (f) PAUB)
Consider the well failure data in Exercise 2-53.Let .4 denote the event that the geological formation has more than 1000 wells and let & denote the event that a well failed. Determine the following probabilities. (a) P(4) (d) P(AUB) (b) PLA') (e) P(B) (c) P(AUB)
Consider the hospital emergency room data in Example 2-8.Let 4 denote the event that a visit is to Hospital 4 and let & denote the event that a visit results in LWBS (at any hospital). Determine the following probabilities. (a) P(AB) (d) P(AUB) (b) P(A') (e) P(A) (c) P(AUB)
Let 4 denote the event that a reaction final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target, Determine the following probabilities. P(A) (a) P(B) (b) (d) P(AUB) (e) PAB) (c) P(AUB)
Consider the endothermic reactions in Exercise
Use the axioms of probability to show the following: (a) For any event E. PE)=1-P(E). (b) P() = 0 (c) If 4 is contained in B, then P(A) = P(B).
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: shock resistance high low scratch high 70 9 resistance low 16 5 The frequency of each type of transaction (in the second column) can be used as the
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. Redox reaction experiments using four different amounts of magnesium powder are performed. Each result may or may not be
A message can follow different paths through servers on a network. The sender's message can go to one of five servers for the first step; each of them can send to five servers at the second step each of those can send to four servers at the third step; and then the message goes to the recipient's
Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0 and 9) fol- lowed by three letters (between 4 and Z). If a license number is selected randomly, what is the probability that yours is the one selected?
In a NiCd battery, a fully charged cell is composed of Nickelic Hydroxide. Nickel is an element that has multiple oxidation states that is usually found in the following states: nickel charge 0 proportions found + 0.17 0.35 0.33 0.15 (a) What is the probability that a cell has at least one of the
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Because acids and bases are usually colorless (as are the water and salt produced in the neutralization reac tion). pH is measured to monitor the reaction. Suppose that the
An injection-molded part is equally likely to be ob tained from any one of the eight cavities on a mold. (a) What is the sample space? (b) What is the probability a part is from cavity 1 or 2? (c) What is the probability that a part is from neither cavity 3 nor 4?
A part selected for testing is equally likely to have been 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
Orders for a computer are summarized by the op- tional features that are requested as follows: no optional features one optional feature more than one optional feature proportion of orders 0.3 0.5 02 (a) What is the probability that an order requests at least one optional feature? (b) What is the
The sample space of a random experiment is (a,b, c, del with probabilities 01.01.07.04, and respectively Let A denote the event (a,b, c), and let B denote the event (c.d. e). Determine the following: (a) P(4) (b) P(B) (c) P(4) (d) P(4) (c) P(B)
Each of the possible five outcomes of a random ex- periment is equally likely. The sample space is (a,b, c,d, e). Let 4 denote the event (a, b), and let 8 denote the event (c,d,e). Determine the following: (a) P(4) (b) P(B) (c) P(A') (d) P(AUB) (e) P(B)
An article in The Journal of Data Science ["A Statistical Analysis of Well Failures in Baltimore County" (2009, Vol. 7.pp. 111-127)] provided the following table of well failures for different geological formation groups in Baltimore County. Wells Geological Formation Group Failed Total Gneiss 170
Consider the hospital emergency department data in Example 2-8.Let A denote the event that a visit is to Hospital 1 and let 8 denote the event that a visit results in admittance to any hospital. Determine the number of persons in each of the following events. (a) 48 (b) (c) AUB (d) AUB (c) B
The following table summarizes 204 endothermic re- actions involving sodium bicarbonate.Final Temperature Conditions 266 K Heat Absorbed (cal) Below Target Above Target 271 K 274 K 12 44 56 40 16 36 Let 4 denote the event that a reaction final temperature is 271 K or less. Let B denote the event
A bin of 50 parts contains five that are defective. A sample of two parts is selected at random, without replace- ment. Determine the probability that both parts in the sample are defective.
Plastic parts produced by an injection-molding opera- tion are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses three parts from among the 12 at random. Two cavi-
In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements. (a) What is the probability that exactly one tank in the
Consider the design of a communication system. (a) How many three-digit phone prefixes that are used to rep- resent 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
In the design of an electromechanical product, 12 components are to be stacked into a cylindrical casing in a manner that 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 de signs
In the laboratory analysis of samples from a chemical process, five samples from the process are analyzed daily. In addition, a control sample is analyzed two times each day to check the calibration of the laboratory instruments. (a) How many different sequences of process and control samples are
In the layout of a printed circuit board for an elec- tronic product, there are 12 different locations that can accom- modate 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
A batch of 140 semiconductor chips is inspected by choosing a sample of five chips. Assume 10 of the chips do not conform to customer requirements. (a) How many different samples are possible? (b) How many samples of five contain exactly one noncon forming chip? (e) How many samples of five contain
A manufacturing operation consists of 10 operations. However, five machining operations must be completed before any of the remaining five assembly operations can begin. Within each set of five, operations can be completed in any order. How many different production sequences are possible?
An order for a computer can specify any one of five memory sizes, any one of three types of displays, and any one of four sizes of a hard disk, and can either include or not include a pen tablet. How many different systems can be ordered?
The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space for the rise time of each batch be positive, real numbers. Consider the rise times of two batches. Let 4 denote the event that the rise time of batch 1 is less than 72.5 minutes, and let B denote the
Counts of the Web pages provided by each of two computer servers in a selected hour of the day are recorded. Let A denote the event that at least 10 pages are provided by server 1 and let B denote the event that at least 20 pages are provided by serve 2.(a) Describe the sample space for the numbers
A sample of two printed circuit boards is selected 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, eight boards with minor defects, and two boards with major defects. (b) The batch
A sample of two items is selected without replace- ment from a batch. Describe the (ordered) sample space for each of the following batches: (a) The batch contains the items (a,b, c,d. (b) The batch contains the items (a,b, c.d...)- (c) The batch contains 4 defective items and 20 good items. (d)
The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space be positive, real numbers. Define the events A and B as follows: A=(xx 52.5). Describe each of the following events: (b) B' (a) A (c) 4B (d) AUB
Samples of emissions from three suppliers are classi fied for conformance to air-quality specifications. The results from 100 samples are summarized as follows: conforms yes 1 22 8 supplier 2 25 5 3 30 10 Let A denote the event that a sample is from supplier 1, and let B denote the event that a
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows: edge finish excellent good surface finish excellent good 80 2 10 8 (a) Let 4 denote the event that a sample has excellent surface
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized below: scratch resistance shock resistance high low high low 70 9 16 5 Let 4 denote the event that a disk has high shock resistance, and let B denote the event
In control replication, cells are replicated over a period of two days. Not until mitosis is completed can freshly synthesized DNA be replicated again. Two control mechanisms have been identified one positive and one negative. Suppose that a replication is observed in three cells. Let A denote the
In light-dependent photosynthesis, light quality refers to the wavelengths of light that are important. The wavelength of a sample of photosynthetically active radiations (PAR) is measured to the nearest nanometer. The red range is 675-700 m and the blue range is 450-500 nm. Let 4 denote the event
Four bits are transmitted over a digital communica- tions channel. Each bit is either distorted or received without distortion. Let 4, denote the event that the ith bit is distorted, 1=1,...4. (a) Describe the sample space for this experiment. (b) Are the 4s mutually exclusive? Describe the
In an injection-molding operation, the length and width, denoted as X and Y, respectively, of each molded part are evaluated. Let A denote the event of 48 < x < 52 centimeters B denote the event of 9 <
In a magnetic storage device, three attempts are made to read data before an error recovery procedure that repositions the magnetic head is used. The error recovery procedure attempts three repositionings before an “abort’’ message is sent to the operator. Let s denote the success of a read
Calls are repeatedly placed to a busy phone line until a connection is achieved.
The time of a chemical reaction is recorded to the nearest millisecond.
The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category is measured by an optical inspection of a sample.
The pH reading of a water sample to the nearest tenth of a unit.
The time until a service transaction is requested of a computer to the nearest millisecond.
The concentration of ozone to the nearest part per billion.
The following two questions appear on an employee survey questionnaire. Each answer is chosen from the fivepoint scale 1 (never), 2, 3, 4, 5 (always).Is the corporation willing to listen to and fairly evaluate new ideas?How often are my coworkers important in my overall job performance?
A scale that displays two decimal places is used to measure material feeds in a chemical plant in tons.
Each of 24 Web sites is classified as containing or not containing banner ads.
The number of hits (views) is recorded at a high-volume Web site in a day.
In the final inspection of electronic power supplies, either units pass or three types of nonconformities might occur:functional, minor, or cosmetic. Three units are inspected.
Understand random variables
Use Bayes’ theorem to calculate conditional probabilities
Determine the independence of events and use independence to calculate probabilities
Interpret and calculate conditional probabilities of events
Calculate the probabilities of joint events such as unions and intersections from the probabilities of individual events

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