You are told that the probability distribution (pdf) for annual rainfall in Memp

Question

You are told that the probability distribution (pdf) for annual rainfall in Memphis is symmetrical, and that the mean value is 54.2 in, while the annual rainfall exceeded 95% of the years is 45.1 in. Determine: 3. (20 pts) a. How frequent is it to have an annual total equal or larger than 54.2 in? b, what is the value of the annual precipitation exceeded 5% of the years? c. Every how many years on average does the value computed in (b) recur? d. If you had 84 years of data, what would be your expectation regarding the number of years in which it rained less than 45 inches?

Explanation / Answer

a) As the distribution is symmetrical, therefore roughly half the frequencies would lie above the mean. Therefore 50% of the years we should have a rainfall greater than the mean value of 54.2 inches.

b) Here we are given that the annual rainfall exceeded 45.1 inches 95% of the time.

45.1 is ( 54.2 - 45.1) = 9.1 inches below mean. Therefore 9.1 inch above mean is computed as: 54.2 + 9.1 = 63.3 inches. Therefore 63.3 inches rainfall is exceeded 5% of the years.

c) Every 100/5 = 20 that is every twentieth year is this rainfall expected to be exceeded

d) Less than 45 inches is about 5% of the times. Therefore in 84 years of data expected number of years with rainfall less than 45 inches is computed as: = 0.05*84 = 4.2 years.

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