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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

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
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
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
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
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
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
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
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?
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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)
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
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
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:
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
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
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.
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
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
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
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
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
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
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
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)
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,
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
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.
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
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
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
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
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
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
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
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
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
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)
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
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
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
Use permutation and combinations to count the number of outcomes in both an event and the sample space
Interpret probabilities and use probabilities of outcomes to calculate probabilities of events in discrete sample spaces
Understand and describe sample spaces and events for random experiments with graphs, tables, lists, or tree diagrams
Discuss how probability and probability models are used in engineering and science
Explain the differences between mechanistic models and empirical models
Identify the advantages that designed experiments have in comparison to other methods of collecting engineering data
Discuss the different methods that engineers use to collect data
Explain the difference between enumerative and analytical studies
Discuss how variability affects the data collected and used for making engineering decisions
Identify the role that statistics can play in the engineering problem-solving process
7. From a conceptual standpoint, how is the Environmental survey item with the weakest contribution to the Cronbach’s alpha different from the other three Environmental items? And how is this

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