Question

Data collected at an airport suggests that an exponential distribution with mean value 2.855 hours is a good model for rainfall duration.

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

Answer 1

The distribution of the duration of rainfall is:

f(x) = , x > 0 and f(x) = 0, o.w.

The probability that the duration is at least 2 hours = P(X >= 2) = = 0.4963. (Ans).

The probability that the duration is at most 3 hours = P(X <= 3) = = 0.6503. (Ans).

The probability that the duration is between 2 and 3 hours = P(2 <= X <= 3) = = 0.1467. (Ans).

The standard deviation of the distribution = mean of the distribution = 2.855.

Hence, the probability that the rainfall duration exceeds the mean by more than 2 standard deviations = P[X > 2.855 + (2 * 2.855)] = P(X > 8.565) = = 0.0498. (Ans).