Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours?
At most
3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard
deviations? (.0498)
c. What is the probability that it is less than the mean value by more than one standard deviation?
(0)
My try:
I got part a) and I am getting 0.668 for b) but answer should be 0.0498 and same for par c). I got 0.236 for part c but it should be 0 according the solution in the back.
Can someone help me with part b and c.
Best Answer
For an exponential with mean $\mu$, the variance is $\mu^2$, so the standard deviation is $\mu$.
b) We want the probability that the duration is $\gt 2.725+2(2.725)$. I expect you can solve this using techniques that you used in a).
c) This asks for the probability a rain event has length $\lt \mu-\mu$, that is, $\lt 0$. That cannot happen.