Statistics Solutions

(All Steps) 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)

  1. (5) If we build the dike 12 feet high, what is the probability that the water will overflow in any given year?
  2. (5) What is the 99 th percentile of the distribution of Y ?
  3. (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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