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


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