Question

An article proposes the Weibull distribution with a 1.817 and B 0.883 as a model for 1-hour significant wave height (m) at a certain site. (a) What is the probability that wave height is at most 0.5 m? (Round your answer to four decimal places.) (b) What is the probability that wave height exceeds its mean value by more than one standard deviation? (Round your answer to four decimal places.) (c) What is the median of the wave-height distribution? (Round your answer to three decimal places.) (d) For 0 < p < 1, give a general expression for the 100pth percentile of the wave-height distribution n(p) using the given values of a and B. n(p)

Answer 1

a)

P(X<0.5) =1-exp(-(0.5/0.883)^1.817)=0.2994

b)

P(X exceeds mean +standard deviation) =0.1622

c)

median =0.883*(-ln(0.5))^1/1.817 =0.722

d)

n(p) =0.883*(-ln(1-p))^1/1.817