The article “On Assessing the Accuracy of Offshore Wind Turbine Reliability-Based Design Loads from the Environmental Contour Method” (Intl. J. of Offshore and Polar Engr., 2005: 132–140) proposes the Weibull distribution with α = 1.817 and β = .863 as a model for 1-hour significant wave height (m) at a certain site.
a. What is the
b. What is the probability that wave height exceeds its
c. What is the
d. For 0 < p < 1, give a general expression for the 100pth percentile of the wave-height distribution.
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Chapter 4 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- Tailings dams are a major feature of the mining industry. They have not been studies extensively from the point of view of statistical reliability, and some of the data are hard to come by. Nevertheless, it is clear that they fail at a higher rate than engineered dams. It is reasonable to assume that their failure is governed by a Weibull distribution with shape parameter B = 1.5. If dams seem to fail at the rate of 0.001 per dam-year, a) What is the mean time to failure (MTTF)? b) What is the value of the scale parameter 0? c) What is the median failure time?arrow_forwardFor a hypothesis test H0:μ=6H0:μ=6 versus H1:μ≠6H1:μ≠6 and variance known, calculate the p-value for the test statistics: (4 d.p.) i) zc=2.05 ii) zc = -1.84 iii) zc = 2.86arrow_forwardThe article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05. This problem is a test on what population parameter? What is the null and alternative hypothesis? What are the Significance level and type of test? What standardized test statistic will be used? What is the standard test statistic? What is the Statistical Decision? What is the statistical decision in the statement form?arrow_forward
- Following are measurements of soil concentrations (in mg /kg) of chromium (Cr) and nickel (Ni) at20 sites in the area of Cleveland, Ohio. These data are taken from the article "Variation in NorthAmerican Regulatory Guidance for Heavy Metal Surface Soil Contamination at Commercial andIndustrial Sites" (A. Jennings and J. Ma, J. Environment Eng, 2007:587-609). Cr: 260 19 36 247 263 319 317 277 319 264 23 29 61 119 33 281 21 35 64 30Ni: 435 377 359 53 38 38 54 188 397 33 92 490 28 35 799 347 321 32 74 508 (a) Construct a histogram for each set of concentrations. (b) Find the 1st, 2nd and 3rd quartiles for the Cr concentrations (c) Find the 1st, 2nd and 3rd quartiles for the Ni concentrations.arrow_forwardThe lowest level of significance to reject the null hypothesis of no linear association between blood pressure and age is: OA: 0.003 OB: 0.05 OC: 0.0002 OD: 0.0001 OE: 0.04arrow_forwardSuppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation .85 (suggested in “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants,” Water Research, 1984: 1169–1174).a. If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.65 and 3.00?b. How large a sample size would be required to ensure that the first probability in part (a) is at least .99?arrow_forward
- The article "Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids" (J. of Aerospace Engr, 1997: 7-15) gave the accompanying data on ultimate load (kN) for two different types of beams. Sample Sample Sample Mean Туре SD Size 33.4 2.2 Fiberglass grid 26 26 42.8 4.3 Commercial carbon grid a. Assuming that the underlying distributions are normal calculate and interpret a 99% CI for the difference between true average load for the fiberglass beams and that for the carbon beams. b. Does the upper limit of the interval you calculated in part (a) give a 99% upper confidence bound for the difference between the two us? If not, calculate such a bound. Does it strongly suggest that true average load for the carbon beams is more than that for the fiberglass beams? Explainarrow_forward1. Analyze the data as a two way factorial design. Johnson and Leone (Statistics and Experimental Design in Engineering and the Physical Sciences, Wiley, 977) describe an experiment to investigate warping of copper plates. The two factors studied were the temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data were as follows: Temperature (°C) 50 75 100 125 40 17, 20 12,9 16, 12 21, 17 Copper Content (%) 60 80 16, 21 18, 13 18, 21 23, 2! 24, 22 17, 12 25, 23 23, 22 100 28, 27 27, 31 30, 23 29, 31arrow_forward4.10.8 An article in Journal of Hydrology ["Use of a Lognor- mal Distribution Model for Estimating Soil Water Retention Curves from Particle-Size Distribution Data" (2006, Vol. 323(1), pp. 325-334)] considered a lognormal distribution model to esti- mate water retention curves for a range of soil textures. The particle-size distribution (in centimeters) was modeled as a log- normal random variable X with 0 = -3.8 and w = 0.7. Determine the following: a. P(X < 0.02) b. Value for x such that P(X ≤ x) = 0.95 c. Mean and variance of Xarrow_forward
- In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung, et al., International Journal of Reliability, Quality, and Safety Engineering, 2001:109–122), the lifetime, in hours, of a certain type of bearing is modeled with the Weibull distribution with parameters α = 2.25 and μ = 4.474 × 10−4. a) Find the probability that a bearing lasts more than 1000 hours. b) Find the probability that a bearing lasts less than 2000 hours. c) Find the median lifetime of a bearing. d) The hazard function is defined in Exercise 8. What is the hazard at t = 2000 hours?arrow_forwardArtificial joints consist of a ceramic ball mounted on a taper. The article "Friction in Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Áspenberg, et al., Proceedings of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient of friction for a push-on load of 2 kN for taper assemblies made from two zirconium alloys and employing three different neck lengths. Five measurements were made for each combination of material and neck length. The results presented in the following table are consistent with the cell means and standard deviations presented in the article. Тарег Material Neck Length Coefficient of Friction CPTI-ZIO2 CPTI-Z:O, CPTI-Z:O, Long TIAlloy-ZrO, Short TiAlloy-ZrO, Medium TiAlloy-ZrO, Long Short 0.254 0.195 0.281 0.289 0.220 Medium 0.196 0.220 0.185 0.259 0.197 0.329 0.481 0.320 0.296 0.178 0.150 0.118 0.158 0.175 0.131 0.180 0.184 0.154 0.156 0.177 0.178 0.198 0.201 0.199 0.210 Compute the main effects and interactions. Construct…arrow_forwardA set of n = 5 pairs of X and Y scores has SSX = 18, SSY = 8, ∑X=5, ∑Y=15, SSCP = 3. What is the Pearson Product Moment correlation for these scores? answers: a) 18/12 = 1.50 b) 18/144 = .125 c) 3/12 = .25 d) 3/144 = .21arrow_forward
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