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Answer :
Final answer:
To find the probability, we need to determine the cumulative distribution function of the uniform distribution and compute the probability that the largest flood will be less than or equal to 39.3 feet. The probability is 0.965. Subtracting this from 1 gives us a probability of 0.035 that the second largest flood will overflow the levee.
Explanation:
To find the probability that the second largest flood in the next 33 years will overflow a levee of height 39.3 feet, we need to find the probability that the largest flood in the next 33 years will be less than or equal to 39.3 feet. Since the annual flood tide X is uniformly distributed over the interval (20,40), we can use the cumulative distribution function (CDF) to find this probability. The CDF of a uniform distribution is given by (x - a) / (b - a), where x is the value of interest, a is the lower bound, and b is the upper bound. Plugging in the values, we have (39.3 - 20) / (40 - 20) = 19.3 / 20 = 0.965. Therefore, the probability that the second largest flood in the next 33 years will overflow the levee is 1 - 0.965 = 0.035.
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