[Solution] Suppose we are planning to build a dike to hold back flood waters. Let the random variable Y be the highest water level in feet in any given
Question: Suppose we are planning to build a dike to hold back flood waters. Let the random variable Y be the highest water level in feet in any given year at the planned dike’s location. Suppose that Y ~ N(10, 4)
- (5) If we build the dike 12 feet high, what is the probability that the water will overflow in any given year?
- (5) What is the 99 th percentile of the distribution of Y ?
- (10) If we build the dike as high as your answer from part (b), what is the probability that the water will overflow at least once in the next 100 years ? Assume that different years yield independent realizations Y 1 , Y 2 , Y 3 , …etc.
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