Monte Carlo Simulation Problem A community is considering improving their dikes along the banks of a river that floods occasionally. Historically, when storms occur, the river's level rises to a crest averaging 10 feet with standard deviation of 2 feet (normally distributed). If the water crest rises above the the current dikes (13 feet), then flooding occurs. The expected flood damage per incident is provided in the table below according to river crest height. The town council is interested in a 10-year damage forecast. A total of 30 storms are expected in the next ten years. River Crest (ft) Damage ($M) 13')? 2. What is the total damage cost (in $M) expected from thirty storms in the next 10 years? = 3. What is the probability that there is no damage (cost $0) from thirty storms in the next 10 years? 4. What is the probability that total damage exceeds $100M from thirty storms in the next 10 years? 5. What is the maximum 10-year cost in your simulation (i.e, how bad can it get in the worst case)? 6. Show a histogram of the 10-year (30 storm) damage cost distribuition for the Monte Carlo 1000 trials. Given the river crest heights are normally distributed, comment on the shape of this distribution.