In a seismic hazard analysis, the magnitude of the earthquake (Richter\'s scale)

Question

In a seismic hazard analysis, the magnitude of the earthquake (Richter's scale) is modeled with a Type II asymptotic distribution of the largest value. In a certain geographical area, data have been collected for 50 years, and the annual maximum values of the earthquake magnitude have a mean value of 4.0 and a standard deviation of 1.4. It is estimated that an earthquake with a magnitude of 7.0 or more will devastate the region. What is the probability that the annual maximum magnitude will be greater than or equal to 7.0? Compute the same probability if Type I is assumed instead of Type II.

Explanation / Answer

mean = 4

, sd = 1.4

Z = (X - 4)/1.4

P(X > 7)

= P(Z >(7 - 4)/1.4)= P(Z > 2.14285) = 0.0161

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