A nuclear facility in a coastal region is built to withstand ocean wave forces. Suppose

the annual maximum wave height of the ocean waves (above the sea level) is a Gamma distributed

random variable with mean height of 4.0 meters and coefficient of variation of 0.8.

a. What is the probability that the wave height will exceed 6 meters in any year?answer 0(.1763)

b. To construct the nuclear facility in a safe manner, an engineer is assigned to compute a

design wave height (above sea level) that will not be exceeded by ocean waves over a 10-

year period with a probability of 95%, i.e., 10-yr reliability = 0.95. Assuming that wave

height exceedances between years are statistically independent, what should be the height

of the design wave above the sea level?answer(19.04 m)

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