Question

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 $\alpha=1.817$ and $\beta=.863$ as a model for 1-h. significant wave height $(\mathrm{m})$ at a certain site. (a) What is the probability that wave height is at most. 5 $\mathrm{m}$ ? (b) What is the probability that wave height exceeds its mean value by more than one standard deviation? (c) What is the median of the wave-height distribution? (d) For $0 < p<1,$ give a general expression for the 100$p$ th percentile of the wave-height distribution.

          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 $\alpha=1.817$ and $\beta=.863$ as a model for 1-h. significant wave height $(\mathrm{m})$ at a certain site.
(a) What is the probability that wave height is at most. 5 $\mathrm{m}$ ?
(b) What is the probability that wave height exceeds its mean value by more than one standard deviation?
(c) What is the median of the wave-height distribution?
(d) For $0 < p<1,$ give a general expression for the 100$p$ th percentile of the wave-height distribution.

Added by Manuela W.

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