Answer
The median waiting time is about 3.5 minutes.
Work Step by Step
To find the median waiting time, we can find $t$ such that $P(0 \leq T \leq t) = 0.5$
$\int_{0}^{t} f(t)~dt = 0.5$
$\int_{0}^{t} 0.2e^{-t/5}~dt = 0.5$
$-e^{-t/5}~\vert_{0}^{t} = 0.5$
$1-e^{-t/5} = 0.5$
$e^{-t/5} = 0.5$
$-t/5 = ln(0.5)$
$t = -5~ln(0.5)$
$t \approx 3.5$
The median waiting time is about 3.5 minutes.
