Chapter 11.2, Problem 58E

In Problems 53 and 58, find the associated cumulative distribution function.

58.    Waiting time. The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function given by

$f\left(x\right)=\{\begin{array}{cc}\frac{1}{2}{e}^{-x/2}& \text{if }x\ge 0\\ 0& \text{otherwise}\end{array}$

(A)    Evaluate ${\displaystyle {\int }_2^{6}f\left(x\right)}$ and interpret the results.

(B)    What is the probability that a customer waits less than 3 minutes?

(C)    What is the probability that a customer waits more than 5 minutes?