# Probability: Other Probability Distributions – #456

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{align} & \frac{1}{4}{{e}^{-x/4}}\text{ if }x\ge 0 \\ & 0\text{ if }x<0 \\ \end{align} \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