A reservoir in the locale of Problem 1 will overfill when the annual precipitation exceeds 30 in. Determine the probability that the reservoir will overfill (a) next year, (b) at least once in three successive years, and (c) in each of three successive years.
Problem 1
The 80-year record of annual precipitation at a midwestern gauge location has a range between 14 in. in 1972 and 42 in. in 2001. The record has a mean of 27.6 in. and a standard deviation of 6.06 in. Assuming a normal distribution, (a) plot the frequency curve on probability paper, (b) determine the probability of a drought worse than the 1972 value, and (c) determine the recurrence interval of the 2001 maximum depth and compare it with the apparent recurrence interval.
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