A weather forecaster predicts that the May rainfall will be

A weather forecaster predicts that the May rainfall will be between 3 and 7 inches but has no idea what the amount will actually be. If it assumed that the actual historic rainfall amount in May is uniformly distributed between 3 and 7 inches, what is the probability that the actual amount will be less than 4 inches?

0.25

0.33

0.75

0.67

Solution

Note that here,          
          
a = lower fence of the distribution =    3      
b = upper fence of the distribution =    7      
          
Note that P(x<c) = P(a<x<c) = (c-a)/(b-a). Thus, as          
          
c = critical value =    4      
          
Then          
          
P(x<4) =    0.25   [ANSWER, A]