1. The return period of very severe sea storms resulting in structural failures
ID: 3335017 • Letter: 1
Question
1. The return period of very severe sea storms resulting in structural failures in a ship is assumed to be 100,000 hours of sailing. Find the probability that a ship will not be damaged in 20,000 hours 2. If during the hours of heavy traffic on a bridge, the traffic is considered random with a volume of 960 vehicles per hour per lane, determine, for this lane, the probability of (a) not more than 3 cars in an interval of 15 seconds, (b) at least 6 cars in the same time interval. (Hint: start by computing the return period for one vehicle) 3. The occurrence of floods in a county follows a Poisson distribution with a return period of 20 years. The damage in each flood is log-normally distributed with a mean of $2 million and a coefficient of variation of 25%. Assume that damage in any one flood is statistically independent of the damage in any other flood. (a) What is the probability of more than two floods occurring in the county during the next 10 years? (b) What is the probability that damage in the next flood will exceed $3 million? (c) What is the probability than none of the floods that could occur in the next 10 years will cause damage exceeding $3 million? 4. Suppose that on an average two tornadoes occur in 10 years in a county in Oklahoma. Further assume that the tornado-generated wind speed can be modeled by a log-normal random variable with a mean of 120 mph and a standard deviation of 12 mph. (a) What is the probability that there will be at least one tornado next year? (b) If a structure in the county is designed for wind speed of 150 mph, what is the probability that the structure will be damaged during such a tornado? (c) What is the probability that the structure will be damaged by tornado next year? (Hint: consider that any number of tornadoes can occur next year) 5. Structures in a county need to be designed for earthquake loading. After a detailed seismic risk analysis of the county, it is observed that the peak ground acceleration A observed in an earthquake event can be modeled by an exponential distribution with a mean of 0.2g. If A exceeds 0.4g, structures in the county will suffer significant damage. Assume that earthquakes occur on the average once every 2 years in the county, and the damage from different earthquakes is statistically independent. (a) What is the probability that there will be exactly two earthquakes in the next 50 years? (b) What is the probability of significant structural damage in an earthquake? (c) What is the probability of no significant structural damage due to earthquakes in a year? (d) What is the probability of no significant structural damage due to earthquakes in the next 50 years?Explanation / Answer
1)
X - the time it takes for failure
X follow exponential distribution with mean = 100,000 hours
P(X > x) = e^(-x/100000)
P(X > 20000) = e^(-20000/100000) = e^(-0.2) = 0.8187307
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