Suppose the time spent by a randomly selected student at a campus computer lab has a gamma distribution with mean 20 minutes and variance 80 minutes.

a. What are the values of $α$ and $β$ ? 

$\mu =\alpha \beta=20$

$\sigma^2=\alpha \beta^2=80$

$\beta=\dfrac{80}{20}=4$

$\alpha=\dfrac{20}{4}=5$

b. What is the probability that a student uses the terminal for at most 24 min?

$P(X\le 24)=F(24;\alpha, \beta)=F(24/\beta;\alpha)$

$=F(24/4;5)=F(6;5)=0.7149$