Answer
$28.854$
Work Step by Step
The probability for $P(X \geq 20)$ can be computed as:
$P(X \geq 20) =\int_{20}^{\infty} \dfrac{1}{r}e^{-x/r} dx \\=\dfrac{1}{r} \lim\limits_{a \to \infty} \int_{20}^{a} e^{-x/r} dx \\=(-1) \lim\limits_{a \to \infty} (\dfrac{1}{e^{a/r}}-e^{-20/8})\\=e^{-20/r}$
We are given that $P(X \geq 20) =\dfrac{1}{2}$
So, we have:
$e^{-20/r}=\dfrac{1}{2}\\\dfrac{20}{r}=\ln 2\\r=\dfrac{20}{\ln 2} \approx 28.854$
