Chapter 9.2, Problem 33E

Using the Exponential Density Function In Exercises 33-36, find the required probabilities using the exponential probability density function

$f\left(t\right)=\frac{1}{\lambda }{e}^{-t\lambda },[0,\infty )$.

Waiting Time The waiting time t (in minutes) for service at the checkout at a grocery store is exponentially distributed with $\lambda =3$. Find the probability of waiting (a) less than 2 minutes, (b) more than 2 minutes but less than 4 minutes, and (c) at least 2 minutes.