9. Ocean wave heights affect a pier in an African port. Wave height affect the forces on the pier. All wave heights are relative to mean seal level.

a) Given that the maximum annual wave heights are Normally distributed and have a mean of 12 ft and a COV of 0.60. For a given year, what is the probability that wave heights will exceed 18 ft?

b) You will be designing the pier for the maximum wave height will not be exceeded with a probability of 90% in 5 years. What would your design value be? Assume that wave heights per year are statistically independent.

c) Given that wave heights follow a Poisson distribution. Waves exceeding 18 ft have a 30% probability of damaging the pier. What is the probability of no damage in 5 years? Pier damage from extreme waves is statistically independent.