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
- Artificial 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_forwardThe article “Hydrogeochemical Characteristics of Groundwater in a Mid-Western CoastalAquifer System” (S. Jeen, J. Kim, et al., Geosciences Journal, 2001:339–348) presentsmeasurements of various properties of shallow groundwater in a certain aquifer system inKorea. Following are measurements of electrical conductivity (in microsiemens percentimeter) for 23 water samples.2099 528 2030 1350 1018 384 14991265 375 424 789 810 522 513488 200 215 486 257 557 260461 500Find the mean.Find the standard deviation.Find the median.Construct a dotplot.Find the 10% trimmed mean.Find the first quartile.Find the third quartile.Find the interquartile range.Construct a boxplot.Which of the points, if any, are outliers?If a histogram were constructed, would it be skewed to the left, skewed to the right, orapproximately symmetric?arrow_forwardA study was conducted in the tidal flat at Polka Point, North Stradbroke Island to examine the distribution of the animals that live with the seagrass Sargassum at different distances from the shoreline. Samples of Sargassum were taken at 5, 10, 15 m from the shore and these were examined for amphipods and isopods. The observations are recorded below. Is the distribution of each of the organisms with regards to the shore the same at all three distances? Use the data below to test the hypothesis at the p < 0.05 level. Clearly state the hypotheses and interpret the results. (Note: Find chi-square for each individual column (amphipods and isopods, not the two together) Distance Amphipods Isopods 5 2 7 10 31 14 15 45 22arrow_forward
- The following data on distilled alcohol content (%) fora sample of 35 port wines was extracted from the article“A Method for the Estimation of Alcohol inFortified Wines Using Hydrometer Baumé andRefractometer Brix” (Amer. J. Enol. Vitic., 2006:486–490). Each value is an average of two duplicatemeasurements. The following data on distilled alcohol content (%) fora sample of 35 port wines was extracted from the article“A Method for the Estimation of Alcohol inFortified Wines Using Hydrometer Baumé andRefractometer Brix” (Amer. J. Enol. Vitic., 2006:486–490). Each value is an average of two duplicatemeasurements. 16.35 18.85 16.20 17.75 19.58 17.73 22.75 23.78 23.2519.08 19.62 19.20 20.05 17.85 19.17 19.48 20.00 19.9717.48 17.15 19.07 19.90 18.68 18.82 19.03 19.45 19.3719.20 18.00 19.60 19.33 21.22 19.50 15.30 22.25Use methods from this chapter, including a boxplot thatshows outliers, to describe and summarize the data.arrow_forward09:52 | 80% o © Lite ital.kemu.ac.ke papti.TICIT ti aliSiti thE answer you obtain, to the blank space provided Question 3 10 pts A fair coin was tossed three times. Let x be the number of heads. Find a) The mean ofx 1.5 b) the variance of x 0.75arrow_forwardThe article "A Probabilistic Analysis of Dissolved Oxygen-Biochemical Oxygen Demand Relationship in Streams" (J. Water Resources Control Fed., 1969: 73-90) reported data on the rate of oxygenation in streams in a certain region. The sample mean and standard deviation were computed as = 0.173 and s= 0.066, respectively. We would like to know if a normal distribution could be a reasonable model for the data. To do this, we have partitioned the quantitative variable into 5 discrete regions and counted the number of streams observed to have oxygenation rates in the given interval. First determine the probability of falling into each region if the normal distribution is the appropriate model. Then use those probabilities with the expected counts to conduct a Chi-squared goodness of fit test. Use a = 0.05. Frequency 12 20 23 15 13 Rate (per day) Below .100 .100 below.150 .150 - below.200 .200 - below .250 .250 or morearrow_forward
- TABLE 15.3 The wing stroke frequencies of two species of Euglossine bees were recorded for a sample of n₁ = 4 Euglossa mandibularis Friese (species 1) and n₂ = 6 Euglossa im- perialis Cockerell (species 2). The frequencies are listed in Table 15.3. Can you con- clude that the distributions of wing strokes differ for these two species? Test using α = .05. Wing Stroke Frequencies for Two Species of Bees Species 1 Species 2. 235 225 190 188 180 169 180 185 178 182arrow_forward5.28 Variable life insurance return rates. Refer to the THEMENTE International Journal of Statistical Distributions (Vol. 1, 2015) P study of a variable life insurance policy, Exercise 4.97 (p. 239). SE HANDE Recall that a ratio (x) of the rates of return on the investment for C SE two consecutive years was shown to have a normal distribution, D PENZI NIMEREN MERC with = 1.5 and o= .2. Consider a random sample of 100 P WWW FESTE! variable life insurance policies and let represent the mean COME ratio for the sample. a. Find E(T) and interpret its value. b. Find Var(z). c. Describe the shape of the sampling distribution of . d. Find the z-score for the value = 1.52. e. Find P(x > 1.52). f. Would your answers to parts a-e change if the rates (x) of return on the investment for two consecutive years was not normally distributed? Explain.arrow_forwardGiven that Y1, Y2, Y3, ..., Yn is a random sample from a gamma distribution with parameters alfa = 3, and Beta = theta, find the mle of theta.arrow_forward
- From the Gaussian error curve, what is the probability that a result From population lies between +o and +20 ? Given that area under Gaussian curve for + o= 68.3% and + 20=95.4% O 30.65 % 20.22 % 13.6% O34.2% O47.7 %arrow_forwardA manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n= 15 shafts is tested and = 2.78. It is known that ơ = 0.9 and that wear is normally distributed. Question 1: Parameter of interest for this test Question 2: Test Ho: µ = 2.5 versus H1: µ ± 2.5, a = 0.05 Question 3: What is the power of the test if true u = 3.10 Question 4: Sample size required to detect a true mean of 3.10 if we wanted the power to be at least 0.9? v Question 1 a. Reject Ho. There is evidence to support the claim that the mean wear differs from 2.5 at a = 0.05 v Question 2 b.0.2670 v Question 3 C. n=24 Question 4 d. Mean wear of crankshafts e. Fail to reject Ho. There is no sufficient evidence to support the claim that the mean wear of crankshafts differs from 2.5 at a = 0.05 f. n15 g. 0.7330arrow_forwardA manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n= 15 shafts is tested and = 2.78. It is known that o = 0.9 and that wear is normally distributed. Question 1: Parameter of interest for this test Question 2: Test Ho: µ = 2.5 versus H1: u + 2.5, a = 0.05 Question 3: What is the power of the test if true u = 3.10 Question 4: Sample size required to detect a true mean of 3.10 if we wanted the power to be at least 0.9? a. Reject Hn. There is evidence to support the claim that the mean wear differs from 2.5 at a = 0.05 Question 1 Question 2 b.ns 15 v Question 3 C.n=24 Question 4 d. 0.7330 e. Mean wear of crankshafts f. Fail to reject Ho- There is no sufficient evidence to support the claim that the mean wear of crankshafts differs from 2.5 at a = 0.05 g 0.2670 >arrow_forward
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