Answer to Question #304187 in Statistics and Probability for ekamanga

Question

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.

Answer 1

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?

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

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