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Probability And Statistics For Engineering And The Sciences 9th Edition Jay L. Devore - Solutions

The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal width classes with boundaries 4000, 4200, .... [The histogram will agree with the one in "Comparison
A transformation of data values by means of some mathematical function, such as ˆšx or 1/x, can often yield a set of numbers that has "nicer" statistical properties than the original data. In particular, it may be possible to find a function for which the histogram of transformed values
Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information on misorientation angle (degrees) was extracted from the article "Observations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy: Crystallographic $Automated electron backscattered diffraction is now being used in the$
The article "Study on the Life Distribution of Microdrills" (J. of Engr. Manufacture, 2002: 301-305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy.a. Why
The accompanying frequency distribution on deposited energy (mJ) was extracted from the article "Experimental Analysis of Laser-Induced Spark Ignition of Lean Turbulent Premixed Flames" (Combustion and Flame, 2013: 1414-1427).a. What proportion of these ignition trials resulted in a deposited
The following categories for type of physical activity involved when an industrial accident occurred appeared in the article "Finding Occupational Accident Patterns in the Extractive Industry Using a Systematic Data Mining Approach" (Reliability Engr. and System Safety, 2012: 108-122):A. Working
Consider the population consisting of all computers of a certain brand and model, and focus on whether a computer needs service while under warranty. a. Pose several probability questions based on selecting a sample of 100 such computers. b. What inferential statistics question might be answered by
A Pareto diagram is a variation of a histogram for categorical data resulting from a quality control study. Each category represents a different type of product nonconformity or production problem. The categories are ordered so that the one with the largest frequency appears on the far left, then
The cumulative frequency and cumulative relative frequency for a particular class interval are the sum of frequencies and relative frequencies, respectively, for that interval and all intervals lying below it. If, for example, there are four intervals with frequencies 9, 16, 13, and 12, then the
Fire load (MJ/m2) is the heat energy that could be released per square meter of floor area by combustion of contents and the structure itself. The article "Fire Loads in Office Buildings" (J. of Structural Engr., 1997: 365-368) gave the following cumulative percentages (read from a graph) for fire
The May 1, 2009, issue of The Montclarian reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):590 815 575 608 350 1285 408 540 555 679a. Calculate and interpret the sample mean and median.b. Suppose the 6th observation had
Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article "Dust Sampling Methods for Endotoxin-An Essential, But Underestimated Issue" (Indoor Air, 2006: 20-27) considered various issues associated with determining endotoxin
Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an industrial by-product, it often finds its way into aquatic systems where it can have deleterious effects on various avian and aquatic species. The accompanying data on
A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape ("Oxygen Consumption and Ventilation During Escape from an Offshore Platform," Ergonomics, 1997: 281-292):a. Construct a stem-and-leaf display of the
The article "Snow Cover and Temperature Relationships in North America and Eurasia" (J. Climate and Applied Meteorology, 1983: 460-469) used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the following
Blood pressure values are often reported to the nearest 5 mmHg (100, 105, 110, etc.). Suppose the actual blood pressure values for nine randomly selected individuals are 118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2 a. What is the median of the reported blood pressure values? b.
The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft ("Statistical Crack
a. Give three different examples of concrete populations and three different examples of hypothetical populations. b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.
Compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures.In Exercise 27The article "Study on the Life Distribution of Microdrills" (J. of Engr. Manufacture, 2002: 301-305) reported the following
A sample of n 5 10 automobiles was selected, and each was subjected to a 5-mph crash test. Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows: S S F S S S F F S S a. What is the value of the sample proportion of successes
a. If a constant c is added to each xi in a sample, yielding yi = xi + c, how do the sample mean and median of the yis relate to the mean and median of the xis? Verify your conjectures. b. If each xi is multiplied by a constant c, yielding yi = cxi, answer the question of part (a). Again, verify
An experiment to study the lifetime (in hours) for a certain type of component involved putting ten components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded. Denote the lifetimes of the two components still
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data
The value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations ("Strength and Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U-1Mo Intermetallic," J. of Materials Engr. and Performance, 1997:
The article "Effects of Short-Term Warming on Low and High Latitude Forest Ant Communities" (Ecoshpere, May 2011, Article 62) described an experiment in which observations on various characteristics were made using minichambers of three different types:(1) Cooler (PVC frames covered with shade
Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one producer to another. In May 2013, the author went to the website klwines.com, randomly selected 10
Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes:a. Determine the value of the sample standard deviation for each sample, interpret these values, and then contrast variability in the two samples.
A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of sclera lamina (mm2) from human optic nerve heads ("Morphometry of Nerve Fiber Bundle Pores in the Optic Nerve Head of the Human,"
Many universities and colleges have instituted supplemental instruction (SI) programs, in which a student facilitator meets regularly with a small group of students enrolled in the course to promote discussion of course material and enhance subject mastery. Suppose that students in a large
The article "A Thin-Film Oxygen Uptake Test for the Evaluation of Automotive Crankcase Lubricants" (Lubric. Engr., 1984: 75-83) reported the following data on oxidation-induction time (min) for various commercial oils:a. Calculate the sample variance and standard deviation. b. If the observations
The first four deviations from the mean in a sample of n = 5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.
A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the
Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two people shaking hands, or a nurse squeezing a patient's forearm to stop bleeding. The article "Investigation of Grip Force, Normal Force, Contact Area, Hand Size, and Handle Size for
Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter.a. Determine the value of the fourth spread. b. Are there any outliers in the sample? Any extreme outliers? c. Construct a boxplot and comment on its features. d. By how much could the largest
The following data on distilled alcohol content (%) for a sample of 35 port wines was extracted from the article "A Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer Baumé and Refractometer Brix" (Amer. J. Enol. Vitic., 2006: 486-490). Each value is an average of two
A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information: Median = 202.2 Lower fourth = 196.0 Upper fourth = 216.8 Three smallest observations ............ 125.8 .............
A company utilizes two different machines to manufacture parts of a certain type. During a single shift, a sample of n = 20 parts produced by each machine is obtained, and the value of a particular critical dimension for each part is determined. The comparative boxplot at the bottom of this page is
Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss
Observations on burst strength (lb/in2) were obtained both for test nozzle closure welds and for production cannister nozzle welds ("Proper Procedures Are the Key to Welding Radioactive Waste Cannisters," Welding J., Aug. 1997: 61-67).Construct a comparative boxplot and comment on interesting
The accompanying comparative boxplot of gasoline vapor coefficients for vehicles in Detroit appeared in the article "Receptor Modeling Approach to VOC Emission Inventory Validation" (J. of Envir. Engr., 1995: 483-490). Discuss any interesting features.
Consider the following information on ultimate tensile strength (lb/in) for a sample of n = 4 hard zirconium copper wire specimens (from "Characterization Methods for Fine Copper Wire," Wire J. Intl., Aug., 1997: 74-80):x̅ = 76,831s = 180Smallest xi = 76,683Largest xi = 77,048Determine the values
A sample of 77 individuals working at a particular office was selected and the noise level (dBA) experienced by each individual was determined, yielding the following data ("Acceptable Noise Levels for Construction Site Offices," Building Serv. Engr. Research and Technology, 2009: 87-94)Use various
Fretting is a wear process that results from tangential oscillatory movements of small amplitude in machine parts. The article "Grease Effect on Fretting Wear of Mild Steel" (Industrial Lubrication and Tribology, 2008: 67-78) included the following data on volume wear (10-4mm3) for base oils having
The accompanying frequency distribution of fracture strength (MPa) observations for ceramic bars fired in a particular kiln appeared in the article "Evaluating Tunnel Kiln Performance" (Amer. Ceramic Soc. Bull., Aug. 1997: 59-63).a. Construct a histogram based on relative frequencies, and comment $The accompanying frequency distribution of fracture strength (MPa) observations for$
A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article "Effects of Short-Term
Aortic stenosis refers to a narrowing of the aortic valve in the heart. The article "Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI" (Annals of Biomed. Engr., 2005: 878-887) gave the following data on aortic root diameter (cm) and gender for a sample of
a. For what value of c is the quantity ∑(xi - c)2 minimized? b. Using the result of part (a), which of the two quantities ∑(xi - )2 and ∑(xi - μ)2 will be smaller than the other (assuming that ≠ μ)?
a. Let a and b be constants and let yi = axi + b for i = 1, 2, . . . , n. What are the relationships between and and between sx2 and sy2? b. A sample of temperatures for initiating a certain chemical reaction yielded a sample average (°C) of 87.3 and a sample standard deviation of 1.04. What
A certain city divides naturally into ten district neighborhoods. How might a real estate appraiser select a sample of single-family homes that could be used as a basis for developing an equation to predict appraised value from characteristics such as age, size, number of bathrooms, distance to the
Elevated energy consumption during exercise continues after the workout ends. Because calories burned after exercise contribute to weight loss and have other consequences, it is important to understand this process. The article "Effect of Weight Training Exercise and Treadmill Exercise on
Here is a description from Minitab of the strength data given in Exercise 13.a. Comment on any interesting features (the quartiles and fourths are virtually identical here). b. Construct a boxplot of the data based on the quartiles, and comment on what you see.
Anxiety disorders and symptoms can often be effectively treated with benzodiazepine medications. It is known that animals exposed to stress exhibit a decrease in benzodiazepine receptor binding in the frontal cortex. The article "Decreased Benzodiazepine Receptor Binding in Prefrontal Cortex in
The mode of a numerical data set is the value that occurs most frequently in the set.a. Determine the mode for the cadence data given in Exercise 73.b. For a categorical sample, how would you define the modal category?In Exercise 73The article "Can We Really Walk Straight?" (Amer. J. of Physical
Specimens of three different types of rope wire were selected, and the fatigue limit (MPa) was determined for each specimen, resulting in the accompanying data.a. Construct a comparative boxplot, and comment on similarities and differences. b. Construct a comparative dotplot (a dotplot for each
The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange, which is the average of the smallest and largest observations, and the midfourth, which is the average of the two fourths.
The authors of the article "Predictive Model for Pitting Corrosion in Buried Oil and Gas Pipelines" (Corrosion, 2009: 332-342) provided the data on which their investigation was based.a. Consider the following sample of 61 observations on maximum pitting depth (mm) of pipeline specimens buried in
Consider a sample x1, x2,..., xn and suppose that the values of , s2, and s have been calculated. a. Let yi = xi - for i = 1,..., n. How do the values of s2 and s for the yi's compare to the corresponding values for the xi's? Explain. b. Let zi = (xi - )/s for i = 1,..., n. What are the values
Let n and sn2 denote the sample mean and variance for the sample x1,..., xn and let n+1 and s2n+1 denote these quantities when an additional observation xn+1 is added to the sample.a. Show how n+1 can be computed from n and xn+1.b. Show thatso that s2n+1 can be computed from xn+1, n, and s2n. c.
The amount of flow through a solenoid valve in an automobile's pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Two different levels (low and high) of each factor
Lengths of bus routes for any particular transit system will typically vary from one route to another. The article "Planning of City Bus Routes" (J. of the Institution of Engineers, 1995: 211-215) gives the following information on lengths (km) for one particular system:a. Draw a histogram
A study carried out to investigate the distribution of total braking time (reaction time plus accelerator-to-brake movement time, in ms) during real driving conditions at 60 km/hr gave the following summary information on the distribution of times ("A Field Study on Braking Responses During
The sample data x1, x2,..., xn sometimes represents a time series, where xt = the observed value of a response variable x at time t. Often the observed series shows a great deal of random variation, which makes it difficult to study longer-term behavior. In such situations, it is desirable to
Consider numerical observations x1,..., xn. It is frequently of interest to know whether the xi s are (at least approximately) symmetrically distributed about some value. If n is at least moderately large, the extent of symmetry can be assessed from a stem-and-leaf display or histogram. However, if
Consider a sample x1, ... , xn with n even. Let L and U denote the average of the smallest n/2 and the largest n/2 observations, respectively. Show that the mean absolute deviation from the median for this sample satisfies ∑ |xi - | / n = (U - L) / 2 Then show that if n is odd and the two
In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, -2, 26, 27, and 31. a. Why are these measurements
Four universities-1, 2, 3, and 4-are participating in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play for the championship, and the two losers will also play. One possible outcome can be denoted by 1324 (1 beats 2 and 3 beats 4 in
a. In Example 2.10, identify three events that are mutually exclusive. b. Suppose there is no outcome common to all three of the events A, B, and C. Are these three events necessarily mutually exclusive? If your answer is yes, explain why; if your answer is no, give a counterexample using the
Jay and Maurice are playing a tennis match. In one particular game, they have reached deuce, which means each player has won three points. To finish the game, one of the two players must get two points ahead of the other. For example, Jay will win if he wins the next two points (JJ), or if Maurice
A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two components does so is .96, and the probability that both components do so is .75. Given that the first
The accompanying table categorizing each student in a sample according to gender and eye color appeared in the article "Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask" (J. of Statistics Educ., 2013, Vol. 21, Num. 2).Suppose that one of these 2026 students is randomly
a. A certain company sends 40% of its overnight mail parcels via express mail service E1. Of these parcels, 2% arrive after the guaranteed delivery time (denote the event "late delivery" by L). If a record of an overnight mailing is randomly selected from the company's file, what is the probability
A company uses three different assembly lines-A1, A2, and A3-to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2's components need rework and 10% of A3's need rework. Suppose that 50% of all components are produced by line A1,
Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of the other 365 days. a. If ten people are randomly selected, what is the probability that all have different birthdays? That at least two have the same
A subject is allowed a sequence of glimpses to detect a target. Let Gi = {the target is detected on the ith glimpse}, with pi = P(Gi). Suppose the Giʹs are independent events, and write an expression for the probability that the target has been detected by the end of the nth glimpse.
In a Little League baseball game, team A's pitcher throws a strike 50% of the time and a ball 50% of the time, successive pitches are independent of one another, and the pitcher never hits a batter. Knowing this, team B's manager has instructed the first batter not to swing at anything. Calculate
Four engineers, A, B, C, and D, have been scheduled for job interviews at 10 a.m. on Friday, January 13, at Random Sampling, Inc. The personnel manager has scheduled the four for interview rooms 1, 2, 3, and 4, respectively. However, the manager's secretary does not know this, so assigns them to
A particular airline has 10 a.m. flights from Chicago to New York, Atlanta, and Los Angeles. Let A denote the event that the New York flight is full and define events B and C analogously for the other two flights. Suppose P(A) = .9, P(B) = .7, P(C) = .8 and the three events are independent. What is
A personnel manager is to interview four candidates for a job. These are ranked 1, 2, 3, and 4 in order of preference and will be interviewed in random order. However, at the conclusion of each interview, the manager will know only how the current candidate compares to those previously interviewed.
Consider four independent events A1, A2, A3, and A4, and let pi = P(Ai) for i = 1,2,3,4. Express the probability that at least one of these four events occurs in terms of the pis, and do the same for the probability that at least two of the events occur.
A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and 3. One slip will be randomly selected. Let A1 = {win prize 1}, A2 = {win prize 2}, and A3 = {win prize 3}. Show that A1 and A2 are
Show that if A1, A2, and A3 are independent events, then P(A1 | A2 ⋂ A3) = P(A1).
Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = .6 and P(B) = .4. a. Could it be the case that P(A ∩ B) = .5? Why or why not? b. From now on, suppose that
A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = .22, P(A2) = .25, P(A3) = .28, P(A1 ∩ A2) = .11, P(A1 ∩ A3) = .05, P(A2 ∩ A3) = .07, P(A1 ∩ A2 ∩ A3) = .01. Express in words each of the following
Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products. a. What is the probability that a randomly selected adult regularly consumes both coffee and soda? b. What is the probability that a randomly
Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain store. a. If the probability that at most one of these purchases an electric dryer is .428, what is the probability that at least two purchase an electric dryer? b. If P(all five purchase
An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses. a. What are the simple events in this ranking experiment, and what
Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) = .30 and P(B) = .50. a. Why is it not the case that P(A) + P(B) = 1? b. Calculate
A wallet contains five $10 bills, four $5 bills, and six $1 bills (nothing larger). If the bills are selected one by one in random order, what is the probability that at least two bills must be selected to obtain a first $10 bill?
Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the numerous types of solder defects (e.g., pad non-wetting, knee visibility, voids) and even the degree to which a joint possesses one or more of these defects. Consequently,
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. a. List all outcomes in the event A that all three vehicles go in the same direction. b. List all outcomes in the
A certain factory operates three different shifts. Over the last year, 200 accidents have occurred at the factory. Some of these can be attributed at least in part to unsafe working conditions, whereas the others are unrelated to working conditions. The accompanying table gives the percentage of
An insurance company offers four different deductible levels-none, low, medium, and high-for its homeowner's policyholders and three different levels-low, medium, and high-for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is .4, the analogous probability for the second signal is .5, and the probability that he must stop at least one of the two signals is .7.
The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are
Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) ≤ P(B). For general A and B, what does this imply about the relationship among P(A ⋂ B), P(A) and P(A ⋃ B)?
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 40% of all purchasers request A, 55% request B, 70% request C, 63% request A or B, 77% request A or C, 80% request B or C, and 85% request A or B or C, determine
A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(A1) = .12 P(A2) = .07 P(A3) = .05 P(A1 ⋃ A2) = .13 P(A1 ⋃ A3) = .14 P(A2 ⋃ A3) = .10 P(A1 ⋂ A2 ⋂ A3) = .01 a. What is the
An academic department with five faculty members-Anderson, Box, Cox, Cramer, and Fisher-must select two of its members to serve on a personnel review committee. Because the work will be time-consuming, no one is anxious to serve, so it is decided that the representatives will be selected by putting
In Exercise 5, suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that a. All three family members are assigned to the same station? b. At most two family members are

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