Data collected at Toronto Pearson International Airport sugg

Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration.

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

b

Solution

x=duration of rainfall.....mean= 2.725

p ( duration of the particular rainfall event at this location is at least 2 hrs ) = p( x >= 2) = 1 - p(x<2)

= e^ (-2 / 2.725 ) = 0.48.....
p(x <= 3) = 1 - e^( -3 / 2.725 ) = 0.6674

p ( 2<x<3) = p ( x <3) - p(x<2) = 0.6674 - 0.52 = 0.147