Concept explainers
Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. The article “Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads” (J. of Envir. Engr., 2008: 247–258) suggested that for a certain time period and location, X 5 nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having
a. What are the mean value and standard deviation of ln(X)?
b. What is the
c. What is the probability that X exceeds its mean value, and why is this probability not .5?
d. Is 17,000 the 95th percentile of the distribution?
Trending nowThis is a popular solution!
Chapter 4 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- The article "Effect of Granular Subbase Thickness on Airfield Pavement Structural Response" (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331-342) presents a study of the amount of surface deflection caused by aircraft landing on an airport runway. A load of 160 kN was applied to a runway surface, and the amount of deflection in mm (y) was measured at various distances in m (x) from the point of application. The results are presented in the following table. y 0.000 3.24 0.305 2.36 0.610 1.42 0.914 0.87 1.219 0.54 1.524 0.34 1.830 0.24 a. Fit the linear model y = Bo + B1x + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = Bo + Bịx + B2x² + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. %3D Fit the cubic model y = Bo + B1x + B2x? + B3x + E. For each coefficient, test the C. hypothesis that the coefficient is equal to 0. d. Which of the models in parts (a)…arrow_forwardFluid inclusions are microscopic volumes of fluid that are trapped in rock during rock formation. The article "Fluid Inclusion Study of Metamorphic Gold-Quartz Veins in Northwestern Nevada, U.S.A.: Characteristics of Tectonically Induced Fluid" (S. Cheong, Geosciences Journal, 2002:103-115) describes the geochemical properties of fluid inclusions in several different veins in northwest Nevada. The following table presents data on the maximum salinity (% NaCi by weight) of inclusions in several rock samples from several areas. Salinity Area Humboldt Range Santa Rosa Range 9.2 10.0 11.2 8.8 5.2 6.1 8.3 Ten Mile 7.9 6.7 9.5 7.3 10.4 7.0 Antelope Range Pine Forest Range 6.7 8.4 9.9 10.5 16.7 17.5 15.3 20.0 Can you conclude that the salinity differs among the areas?arrow_forwardQ3) An experiment was carried out to investigate variation of solubility of chemical X in water. The quantities in kg that dissolved in 1 liter at various temperatures are show in the table (1). Table (1) Temperature C Mass of X 2.1 2.6 2.9 3.3 15 20 25 30 35 4 50 5.1 70 7 Use the proper methods to answer the following questions: a) Draw a scatter diagram to show the data. b) Estimate the temperature based on the mass of X. c) What quantity might be expected to dissolve at 42 C? Find the quantity that your cquation indicates would dissolve at 10 C and comment on your answer.arrow_forward
- The depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forwardThe efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.arrow_forwardIn "Orthogonal Design for Process Optimization and Its Application to Plasma Etching" (Solid State Technology, May 1987), G. Z. Yin and D. W. Jillie describe an experiment to determine the effect of C2Fe flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below. Observations C„F. Flow (SCCM) 2 3 4 5 125 2.5 4.4 2.6 3.2 3.2 4.0 160 4.8 4.4 4.8 4.2 3.6 4.2 200 4.6 3.3 2.8 3.4 4.2 5.3 (a) Does C,F, flow rate affect etch uniformity? Construct box plots to compare the factor levels and perform the analysis of variance. Use a = 0.05. There is that flow rate affects etch uniformity. (b) Do the residuals indicate any problems with the underlying assumptions? No. Statistical Tables and Charts Yes.arrow_forward
- The article "Two Different Approaches for RDC Modelling When Simulating a Solvent Deasphalting Plant" (J. Aparicio, M. Heronimo, et al., Computers and Chemical Engineering, 2002:1369–1377) reports flow rate (in dmh) and specific gravity measurements for a sample of paraffinic hydrocarbons. The natural logs of the flow rates (y) and the specific gravity measurements (x) are presented in the following table. х -1.204 0.8139 -0.580 0.8171 0.049 0.8202 0 673 0.8233 1.311 0.8264 1.959 0.8294 2.614 0.8323 3.270 0.8352 Fit the linear model y = Bo + B,x + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. Fit the quadratic model y = Bo + B,x + B2x? + E. For each coefficient, test the a. b. hypothesis that the coefficient is equal to 0. Fit the cubic model y = Bo + Bix + B2x² + Bax + E. For each coefficient, test the C. hypothesis that the coefficient is equal to 0. Which of the models in parts (a) through (c) is the most appropriate? Explain. Using the most…arrow_forwardThe article "Modeling Resilient Modulus and Temperature Correction for Saudi Roads" (H. Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298– 305) describes a study designed to predict the resilient modulus of pavement from physical properties. The following table presents data for the resilient modulus at 40°Cin10® kPa (y), the surface area of the aggregate in m²/kg (x1), and the softening point of the asphalt in °C (х). y X1 X2 1.48 5.77 60.5 1.70 7.45 74.2 2.03 8.14 67.6 2.86 8.73 70.0 2.43 7.12 64.6 3.06 6.89 65.3 2.44 8.64 66.2 1.29 6.58 64.1 3.53 9.10 68.6 1.04 8.06 58.8 1.88 5.93 63.2 1.90 8.17 62.1 1.76 9.84 68.9 2.82 7.17 72.2 1.00 7.78 54.1 The full quadratic model is y = + P,x, + PzX, + Pz*jXz + Pxx¡ + Bzx; + €. Which submodel of this full model do you believe is most appropriate? Justify your answer by fitting two or more models and comparing the results.arrow_forward4. A study to assess the capability of subsurface flow wetland systems to remove biochemical oxygen demand (BOD) and various other chemical constituents resulted in the accompanying data on z = BOD mass loading (kg/ha/d) and y = BOD mass removal (kg/ha/d) ("Subsurface Flow Wetlands-A Performance Evaluation." Water Envir. Res., 1995: 244-247). x Y 11 8 13 16 27 10 11 16 142 35 38 44 103 30 90 75 31 30 26 21 n = 10; Σ | n = 450; Σα" = 37653; Σy = 318; Σ y = 17244; Σ =y = 25344 Answer the following questions: (a) Plot an appropriate graph for the data. (b) Obtain the best lincar prediction equation. (c) For every additional unit change in BOD mass loading, by how much does the BOD mass removal change, on average? (d) Give the value of the statistic that measures the linear association between the BOD mass loading and BOD mass removal. Comment. (e) What percent of variation in the BOD mass removal is explained by the variation by the BOD mass loading? (f) Predict the BOD mass removal,…arrow_forward
- The article “Some Parameters of the Population Biology of Spotted Flounder (Ciutharuslinguatula Linnaeus, 1758) in Edremit Bay (North Aegean Sea)” (D. Türker, B. Bayhan, etal., Turkish Journal of Veterinary and Animal Science, 2005:1013–1018) models therelationship between weight W and length L of spotted flounder as W = aLb where a and bare constants to be estimated from data. Transform this equation to produce a linear model.arrow_forwardThe decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −89.010 16.720 −5.324 0.000 Length 0.704 0.049 14.333 0.000 Using this information, give the equation of the least squares regression line.arrow_forwardAccumulation of mercury (Hg) in fish is hypothesized to correlate with the fish size. Barbonymus schwanenfeldii is a species commonly found in a dam in Sarawak. Table 1 shows data of Hg concentration (mg/kg) present in three sizes of fish caught in the dam in triplicates. (i, ii, iii was already answered.)arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman