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statistics for engineers and scientists
Probability And Statistics For Engineers 5th Edition Richard L Scheaffer, Madhuri Mulekar, James T McClave, Cecie Starr - Solutions
4.26 An assembly operation for a computer circuit board consists of four operations that can be performed in any order.a In how many ways can the assembly operation be performed?b One of the operations involves soldering wire to a microchip. If all possible assembly orderings are equally likely,
4.25 A firm is placing three orders for supplies among five different distributors. Each order is randomly assigned to one of the distributors, and a distributor can receive multiple orders. Find the following probabilities a All orders go to different distributors.b All orders go to the same
4.24 For a certain style of new automobile, the colors blue, white, black, and green are in equal demand.Three successive orders are placed for automobiles of this style. Find the following probabilities a One blue, one white, and one green are ordered.b Two blues are ordered.c At least one black
4.23 Five employees of a firm are ranked from 1 to 5 based on their ability to program a computer.Three of these employees are selected to fill equivalent programming jobs. If all possible choices of three (out of the five) are equally likely, find the following probabilities a The employee ranked
4.22 Show that.
4.21 A fleet of eight taxis is to be randomly assigned to three airports A, B, and C, with two going to A, five to B, and one to C.a In how many ways can this be done?b What is the probability that the specific cab driven by Jones is assigned to airport C?
4.20 How many four-digit serial numbers can be formed if no digit is to be repeated within any one number? (The first digit may be a zero.)
4.19 A package of six light bulbs contains two defective bulbs. If three bulbs are selected for use, find the probability that none is defective.
4.18 Seven applicants have applied for two jobs. How many ways can the jobs be filled if a The first person chosen receives a higher salary than the second?b There are no differences between the jobs?
4.17 Among five portable generators produced by an assembly line in one day, there are two defectives.If two generators are selected for sale, find the probability that both will be nondefective.(Assume the two selected for sale are chosen so that every possible sample of size two has the same
4.16 A corporation has two construction contracts that are to be assigned to one or more of three firms (say I, II, and III) bidding for these contracts.(One firm could receive both contracts.)a List the possible outcomes for the assignment of contracts to the firms.b If all outcomes are equally
4.15 A commercial building is designed with two entrances, door I and door II. Two customers arrive and enter the building.a List the elements of a sample space for this observational experiment.b If all elements in part (a) are equally likely, find the probability that both customers use door I;
4.14 Two vehicles in succession are observed moving through the intersection of two streets.a List the possible outcomes, assuming each vehicle can go straight, turn right, or turn left.b Assuming the outcomes to be equally likely, find the probability that at least one vehicle turns left. (Would
4.13 Hydraulic assemblies for landing gear coming from an aircraft rework facility are inspected for defects. History shows that 8% have defects in the shafts alone, 6% have defects in the bushings alone, and 2% have defects in both the shafts and the bushings. If a randomly chosen assembly is to
4.12 Information on modes of transportation for coal leaving the Appalachian region is shown in Figure 4.11. If coal arriving at a certain power plant comes from this region, find the probability that it was transported out of the region using each of these modes of transportation a By track to
4.11 For volunteers coming into a blood center, 1 in 3 have O blood, 1 in 15 have O, 1 in 3 have A, and 1 in 16 have A. What is the probability that the first person who shows up tomorrow to donate blood has each of these blood types a Type O blood b Type O blood c Type A blood d Either type
4.10 A manufacturing company has two retail outlets.It is known that 30% of the potential customers buy products from outlet I alone, 50% buy from outlet II alone, 10% buy from both I and II, and 10% buy from neither. Let A denote the event that a potential customer, randomly chosen, buys from I
4.9 A vehicle arriving at an intersection can turn left or continue straight ahead. Suppose an experiment consists of observing the movement of one vehicle at this intersection, and do the following.a List the elements of a sample space.b Attach probabilities to these elements if all possible
4.8 How good is your intuition about probability?Look at the following situations and answer the questions without making any calculations. Rely on your intuition, and see what happens.a A six-sided balanced die has four sides colored green and two colored red.Three sequences of tosses resulted in
4.7 For each of the following situations, discuss whether the term probability seems to be used correctly and, if so, how such a probability might have been determined.a A physician prescribes a medication for an infection but says that there is a probability of 0.2 that it will cause an upset
4.6 Use Venn diagrams to verify De Morgan’s Laws.
4.5 Use Venn diagrams to verify the distributive laws.
4.4 Five applicants (Jim, Don, Mary, Sue, and Nancy)are available for two identical jobs. A supervisor selects two applicants to fill these jobs.a List all possible ways in which the jobs can be filled. (That is, list all possible selections of two applicants from the five.)b Let A denote the set
4.3 Construct a table to display the data in Exercise 4.2.
4.2 Of 25 microcomputers available in a supply room, 10 have circuit boards for a printer, 5 have circuit boards for a modem, and 13 have neither type of board. Using P to denote those that have printer boards and M to denote those that have modem boards, symbolically denote the following sets, and
4.1 Of the 2.7 million engineers in the United States(as of 1988), 95.5% are male. In addition, 90.6%are white, 1.6% are black, 5.6% are Asian, 0.4%are Native American. Of the 0.7 million computer specialists, 69.1% are male, 88.3% are white, 3.7% are black, 6.6% are Asian, and 0.1% are Native
3.26 A pediatric surgeon has known from experience that children undergoing any planned surgeries tend to suffer from surgery jitters. Typically, children are given some sedatives or anti-anxiety drugs to calm them down. But this surgeon interested in some new ways to make surgery less frightening
3.25 Too little sleep raises obesity risk, reported Mobile Register, November 17, 2005. A study involving about 18,000 adults participating in the federal government’s National Health and Nutrition Examination Survey (NHANES) throughout the 1980s. Those who get less than 4 hours of sleep a night
3.24 With decreased natural fuel supplies and rising costs, in recent years more and more car manufacturers are switching to hybrid technology. The traditional vehicles draw power from either a gas or diesel engine. Hybrids, however, draw power from two energy sources, typically a gas or diesel
3.23 Coffee may not affect blood pressure in women, reported an article in Mobile Register, November 9, 2005. This article was based on a study reported by the Journal of the American Medical Association (2005) that followed 155,594 mostly white female nurses, age 55 on the average, who took part
3.22 The adult smoking rate declined, according to an article in Mobile Register, November 11, 2005.The reported results were based on a national household survey of 31,326 adults. People were defined as current smokers if they had smoked at least 100 cigarettes in their lifetime and said they
3.21 According to an article in Mobile Register (Study:Breast-feeding may prevent diabetes in moms as well as babies), a new study published in the Journal of the American Medical Association on November 23, 2005, reported results of a long-running health study. In this study that began in 1976,
3.20 The investigators from Exercise 3.19 suspected that in addition to temperature, the yield might also depend on the speed of the mixer. Along with temperatures 100°F, 150°F, and 200°F, they decided to compare two different speeds of the mixer, 1,200 and 1,800 rpm (revolutions per minute).a
3.19 The yield of a particular chemical reaction depends on the temperature at which the reaction is carried out. The investigators are interested in comparing the yield at temperatures 100°F, 150°F, and 200°F. They can conduct a reaction 12 times in an 8-hour shift.a Identify the response
3.18 In the 1990s, scientists became concerned about worldwide declines in the population sizes for amphibians. It was thought that one of the possible causes was the increasing amount of ultraviolet (UV) light to which the eggs were exposed, as many amphibians lay their eggs in shallow water fully
3.17 A utility company is interested in comparing the effect of peak hour rates (dollars per kilowatt of usage) on the electricity usage by small manufacturing businesses.a Describe a design for this experiment, using a sample of 30 small manufacturing businesses for a large industrial complex.b
3.16 Suppose it is possible to determine the wear rate analytically, that is, by using formulas that establish the relation between temperatures and wear rate. However, the engineer is not sure how closely the analytical method estimates the experimental wear rate. He is considering using a range
3.15 A civil engineer is interested in comparing the wear rate of one type of propellant at 600°C, 800°C, and 100°C. Design an experiment to compare the mean wear rate at the three different temperatures.
3.14 An engineering department chair is interested in comparing the effect on the student grades of a well-established postgraduate module delivered using a traditional lecture mode and new distance-learning software. Fifty students enrolled in a postgraduate course are available for this study.a
3.13 Suppose engineers at an environmental testing firm received a project to compare mean percolation rates (mm/yr) for four different cover types used in landfills. Twelve different landfills located in areas comparable in terms of atmospheric temperatures are available for their experiment.Four
3.12 Decide whether these sampling methods produce a simple random sample of students from a class of 30 students. If not, explain why not.a Select the first six students on the class roll sheet.b Pick a digit at random and select those students whose phone number ends in that digit.c If the
3.11 How does Nielsen determine who is watching what show? The determination comes from the data recorded in a journal by members of a Nielsen household. When a person begins to watch a show, he or she is supposed to log on.Computer vision researchers at the University of Florida are developing a
3.10 “Why did they take my favorite show off the air?”The answer lies, no doubt, in low Nielsen ratings.What is the powerful rating system, anyway? Of the 92.1 million households in America, Nielsen Media Research randomly samples 4,000 on which to base their ratings. The sampling design is
3.9 “Food survey data all wrong?” This was the headline of a newspaper article on a report from the from the General Accounting Office of the U.S. Government related to the Nationwide Food Consumption Survey. The survey of 6,000 household of all incomes and 3,600 low-income households is
3.8 Readers of the magazine Popular Science were asked to phone in (on a 900 number) their responses to the following question: Should the United States build more fossil fuel–generating plants or the new so-called safe nuclear generators to meet the energy crisis of the ’90s? Of the total
3.7 Bias is the tendency for a whole set of responses to read high or low because of some inherent difficulty with the measurement process. (A chipped die may have a bias toward 6’s, in that it comes up 6 much more often than we would expect.) In the study of HIV-related risk groups discussed
2.65 Industries use displacement washing with solvent to separate solutes from the voids in a porous medium. Tarleton, Wakeman, and Liang (Trans IchemE, 2003) developed a new technique to improve separation of solid–liquid mixture, using an electric field during washing.They recorded zeta
2.64 Pfeifer, Schubert, Liauw, and Emig (Trans IchemE, 2003) studied temperature measured when using different number of thermocouple holes. They set the reactor temperature to 310°C and measured the temperature on the top cover plate of the reactor, using two different electric controls (grouping
2.63 Table below gives the number of households in the United States for the years 1970 to 2002(U.S. Census Bureau).a Make a time series plot. Comment on the trend observed over the years 1970 to 2002.b Consider percent of households by size during years 1900 and 2000, listed in table below. Make
2.62 Table 2.20 gives the median annual earnings (in constant 2000 dollars) of all wage and salary workers ages 25–34, by sex and educational attainment level (The Condition of Education, 2000).a For bachelor’s degree or higher, plot earnings of male workers against the year and earnings of
2.61 Timely assessment of cracks in steam generator tubes is important for extending the life of nuclear steam generators. Wang and Reinhardt(J. Pressure Vessel Technology, 2003) studied the failure assessment of a steam generator tube with defects, using a finite element method.For different
2.60 Moles et al. (Chem Engg Research & Design, 2003) studied how computation times of the stochastic methods are reduced using parallel implementation of different optimization methods or parallel processors. Their data about the number of parallel processors used and the corresponding
2.59 Rigid structures suffer substantial damage due to effects of structural vibrations from natural disasters such as high winds or earth’s tremors.The variable-orifice dampers are used in high-rise structures to provide a mechanically simple and low-power means to protect structures against
2.58 One of the problems in fluid dynamics is determining pressure in narrow and non-narrow regions through which fluid flows. It is a function of several parameters, including boundary conditions on mass and momentum flux. Stay and Barocas (Int’l J. for Numerical Methods in Fluids, 2003)
2.57 In the United States, the Environmental Protection Agency is charged with the job of monitoring the nation’s environment, that is, air, water, and soil. Some of the major indicators of air quality are levels of carbon monoxide (CO), lead (Pb), nitrogen dioxide (NO2), ozone, and sulfur
2.56 Table 2.19 gives the median annual earnings (in constant 2000 dollars) of all wage and salary workers of ages 25–34, by gender (The Condition of Education, 2000).
2.55 Tidal force is the main hydrodynamic force in estuaries. Shi et al. (Int. J. Numer. Meth. Fluids, 2003) reported the recorded six different measurements of the relative depth of water (y) and tidal velocities (x) at stations 16 and 18 at 9:00 PM on August 12, 1978. The data reported(read from
2.54 Tidal force is the main hydrodynamic force in estuaries. Shi et al. (Int. J. Numer. Meth. Fluids, 2003) reported the recorded tidal elevations(in meters) at stations 16 and 18 at the North Passage of Changing Estuary (read from graphs).The pairs of tidal elevations recorded from 2:00 PM till
2.51 Table below lists the U.S. retail gasoline price(cents per gallon) and U.S. FOB cost of crude oil(dollars per barrel) as reported by the U.S.Energy Information Administration (http://www.eia.doe.gov/).a Construct a scatterplot of gasoline prices versus crude oil prices. Describe the nature of
2.50 Refer to data on the length and weight of largemouth bass analyzed in Exercise 2.34.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.49 Refer to data on density and % body fat analyzed in Exercise 2.33.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.48 Refer to data on age and diameter of oak trees analyzed in Exercise 2.32.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.47 Refer to the ranking data analyzed in Exercise 2.31.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.46 Refer to the RSF data analyzed in Exercise 2.30.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.45 Refer to the tax revenue data analyzed in Exercise 2.29.a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.44 For the relationship developed for the traffic safety data in Exercise 2.28, a Construct a residual plot.b Comment on the shape of the residual plot.c Comment on the appropriateness of the linear relation developed for these data.
2.43 Note that the regression lines of Exercise 2.41 and 2.42 both have positive slopes. How might the value for the correlation coefficient, calculated in Exercise 2.42 part (a), be related to this phenomenon?
2.42 Refer to Exercise 2.40 a Calculate the correlation coefficient r between the county population density x1 and the number of law enforcement employees x2.b Does the correlation between x1 and x2 differ significantly from zero? Test by using .
2.41 Repeat the instruction of Exercise 2.40, except let the independent variable be the number x2 of county law enforcement employees.
2.40 A problem of both economic and social concern in the United States is the importation and sale of illicit drugs. The data shown in Table 2.16 are a part of a larger body of data collected by the Florida Attorney General’s Office in a attempt to relate the incidence of drug seizures and drug
2.39 In the summer of 1981, the Minnesota Department of Transportation installed a stateof-the-art weigh-in-motion scale in the concrete surface of the eastbound lanes of Interstate 494 in Bloomington, Minnesota, The system is computerized and monitors traffic continuously. It is capable of
2.38 Refer to the largemouth bass data in Exercise 2.34.a Compute r and values.b Interpret your answers in part (a) in terms of the relationship between length and weight.
2.37 Refer to the body density data in Exercise 2.33.a Compute r and values.b Interpret your answers in part (a) in terms of the relationship between body fat and body density.
2.36 Refer to the oak tree data in Exercise 2.32.a Compute r and values.b Interpret your answers in part (a) in terms of the variables being measured.
2.35 To measure the effect of certain toxicants found in water, concentrations that kill 50% of the fish in a tank over a fixed period of time (LC50s) are determined in laboratories. There are two methods for conducting these experiments. One method has water continuously flowing through the tanks,
2.34 Table below lists the weight (in pounds) and length(in inches) for 11 largemouth bass (Source: The Mathematics Teacher, 1997, p. 666).a Find a simple linear regression model for predicting the weight of a largemouth bass from knowledge of its length. Do you see any problems in using this
2.33 Good measures of body fat are difficult to come by, but a good measure of body density can be made from underwater weighing. Table below lists the percent fat and body density of 15 women (Source: Pollock, unpublished research report, University of Florida, 1956).a Construct a scatterplot of
2.32 Chapman and Demeritt (Elements of Forest Mensuration, 2nd ed., Albany, NY, J.B. Lyon Company [now Williams Press], 1936) reported diameters (in inches) and ages (in years) of oak trees. The data are shown in table below.a Make a scatterplot. Is there any association between the age of the oak
2.31 Refer to the ranking data from Table 2.13.a Find a simple linear model for the relationship between the ranking by professors and that by executives.b Interpret the slope of the regression line in terms of the problem.c What do you expect the executive’s rank to be if the professor gave a
2.30 Refer to the RSF data from Exercise 2.18.a Find a simple linear model for the relationship(s) using the least-squares technique if the association between the measured and calculated values appears to be linear.b Should we use linear relation to estimate the relation between the measured and
2.29 Refer to the tax revenue data from Table 1.10 and Exercise 2.17.a Remove Alaska from the dataset. Model the relationship between per capita expenditure and per capita tax revenue using the leastsquares technique and a simple linear model.b Interpret the slope of the model in part (a) in terms
2.28 Refer to traffic safety data given in Exercise 2.14.a Model the relationships between 2002 and 1980 traffic deaths using the least-squares technique, if the association between the two variables being studied appears to be linear.b Interpret the slope of the simple linear model in terms of the
2.27 Zsaki et al. (International J. for Numerical Methods in Fluids, 2003) studied the solution to the vector Laplacian system (inner system)using the finite element tearing and interconnecting(FETI) method. They used different mesh sizes from 1/48 to 1/8 to search across the entire computation
2.26 Refer to the refined oil import and export data in Exercise 2.20.a Is there any association between the amount of import and export of refined oil products by the United States?b Make a time series plot showing trend in import and export. Discuss your findings from the time series plot.c
2.25 Refer to the managerial skill/knowledge data of Exercise 2.13. Is there any association between the professors’ and executives’ opinions about the importance of technology management knowledge and skills? Justify your answer.
2.24 Refer to the burst pressure (RSF) data for industrial cylinders reported in Exercise 2.18.a Calculate the correlation between the measured and calculated RSF.b Is there any association between the measured and calculated RSF? Justify your answer.c Does the nature or strength of association
2.23 Refer to the tax revenue data of Table 1.10 and the plot of Exercise 2.17.a Compute a correlation matrix for revenue, taxes, and expenditure.b Interpret correlation coefficients in terms of the problem.c Which variables have the strongest association?Justify your answer.d Are there any
2.22 Refer to the index of industrial production data in Table 1.9.a Calculate correlation between the index of industrial production in 1990 and 1998.b Interpret this correlation in terms of the problem.c Refer to your scatterplot in Exercise 2.16.Does it support your conclusion from the
2.21 Refer to the traffic safety data of Exercise 2.14.a Calculate the correlation between the number of motor vehicle deaths in 1980 and 2002.b Interpret this correlation in terms of the problem.c Refer to your scatterplot in Exercise 2.14.What conclusions can you make from the scatterplot that
2.20 Table below gives the average amount of refined oil products imported and exported per day over the years 1990–2000 (U.S. Census Bureau, Statistical Abstract of the United States, 2001). The averages are reported in 1,000 barrels (bbl) per day, where a barrel contains42 gallons.a Make time
2.15 The longer you stay in school, the more you eventually earn! True? Explore the data of Table 2.12 to see whether it appears to support this claim. Educational attainment is turned into an approximate number to simplify the statistical analysis.a Construct a scatterplot of median weekly
2.14 Are highways getting safer? How can we begin to measure possible improvements in the travel by motor vehicle? One possibility is to study traffic safety data for any discernable patterns or trends.The motor vehicle death rates per 100 million miles driven in the 50 states plus the District of
2.13 Table 2.8 gives the age-adjusted deaths per 100,000 population from 1960 to 2001 (U.S.Census Bureau, Statistical Abstract of the United States, 2003) for the leading disease causes.Construct a time series plot for each cause and comment on how the patterns compare.
2.12 Table below gives the crude oil prices in U.S.dollars per barrel for years 1975–2006 (U.S.Census Bureau, Statistical Abstract of the United States, 2008).a Display this data using a time series plot.b Identify any trends in the crude oil prices.c Identify any peaks or troughs or sudden
2.11 Table below gives data on the urban and rural federal-aid highways (in thousand miles) as reported by the U.S. Census Bureau’s Statistical Abstract of the United States (2001). Federal-aid highways are the highways constructed using funding from the federal government.a Construct time series
2.10 Table below gives (in thousands) the number of state motor vehicle registrations for the United States. Construct a time series plot and describe the trend observed. Year Vehicles Year Vehicles 1925 20,069 1945 31,035 1930 26,750 1950 49,162 1935 26,546 1955 62,689 1940 32,453 1960 73,858 1965
2.9 Table below gives the total U.S. consumption and conventional hydroelectric power consumption(in quadrillion Btu). The data were reported by the U.S. Census Bureau’s Statistical Abstract of the United States (2001).a Construct a time series plot for total U.S.energy consumption.b Compare and
2.8 Table 2.7 gives data on research and development(R&D) expenditures (in millions of dollars)by industry and universities (U.S. Census Bureau, Statistical Abstract of the United States, 2008). Because there are other sources of funds, such as Federal government and nonprofit organizations not
2.7 Table 2.6 gives the average fuel prices (in dollars per Btu) for four different sectors from 1970 to 2004 (U.S. Census Bureau, Statistical Abstract of the United States, 2008).a Construct a time series plot for energy cost for each sector.b Compare and comment on any trends observed.
2.6 Table 2.5 gives the vehicle accident data for different types of trucks (U.S. Census Bureau, Statistical Abstract of the United States, 2003).a Construct a time series plot for each type of vehicle.b Compare and comment on any trends observed.
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