3. An offshore platform is built to withstand ocean wave forces. a) The annual maximum wave height of the ocean waves (above mean sea level) is a random variable with a Gaussian (normal) distribution having a mean height of 4.5 m and a coefficient of variation of 0.60. What is the probability that the wave height will exceed 6.0 m in a given year? b) If the platform were to be designed for a wave height (above mean sea level) such that it will not be exceeded over a period of 3 years with a probability of 70%, what should be the platform height above the mean sea level? (Wave exceedances between years are assumed to be statistically independent). c) Suppose that ocean waves exceeding 6 meters will occur according to a Poisson process and each of these waves could potentially cause damage to the platform with a probability of 0.30. What is the probability that there will be no damage to the platform in the next 3 years? (Damages to the platform between waves are statistically independent).
3. An offshore platform is built to withstand ocean wave forces. a) The annual maximum wave height of the ocean waves (above mean sea level) is a random variable with a Gaussian (normal) distribution having a mean height of 4.5 m and a coefficient of variation of 0.60. What is the probability that the wave height will exceed 6.0 m in a given year? b) If the platform were to be designed for a wave height (above mean sea level) such that it will not be exceeded over a period of 3 years with a probability of 70%, what should be the platform height above the mean sea level? (Wave exceedances between years are assumed to be statistically independent). c) Suppose that ocean waves exceeding 6 meters will occur according to a Poisson process and each of these waves could potentially cause damage to the platform with a probability of 0.30. What is the probability that there will be no damage to the platform in the next 3 years? (Damages to the platform between waves are statistically independent).
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:3. An offshore platform is built to withstand ocean wave forces.
a) The annual maximum wave height of the ocean waves (above mean sea level) is a random variable with a
Gaussian (normal) distribution having a mean height of 4.5 m and a coefficient of variation of 0.60. What is
the probability that the wave height will exceed 6.0 m in a given year?
b) If the platform were to be designed for a wave height (above mean sea level) such that it will not be exceeded
over a period of 3 years with a probability of 70%, what should be the platform height above the mean sea
level? (Wave exceedances between years are assumed to be statistically independent).
c) Suppose that ocean waves exceeding 6 meters will occur according to a Poisson process and each of these
waves could potentially cause damage to the platform with a probability of 0.30. What is the probability that
there will be no damage to the platform in the next 3 years? (Damages to the platform between waves are
statistically independent).
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