The average time between incoming calls at a switchboard is

The average time between incoming calls at a switchboard is 3 minutes. The probability F of waiting less that t minutes until the next incoming call is approximated by the model f(t)=1-e^-t/3 . Find the probability that the next call will be within a) 1/2 minutes and b) 2 minutes

Solution

Given, f(t)=1-e^^-t/3

(a)Therfore, f(1/2)=1-e^(-(1/2)/3)=1-e^(-1/6)=0.1535

And (b) f(2)=1-e^(-2/3)=0.4865