Question: Suppose the time \(X\) a customer must spend waiting in line at a certain bank is a random variable that is exponentially distributed with density function

\[f(x)=\left\{ \begin{aligned} & \frac{1}{4}{{e}^{-x/4}}\text{ if }x\ge 0 \\ & 0\text{ if }x<0 \\ \end{aligned} \right.\]

where \(x\) is the number of minutes a randomly selected customer is in line. Find the probability that a customer will have to stand in line at least eight minutes