The beta distribution takes a value between 0 and 1.
The proportion of 2 days relative to max of 2.5 days is 2/2.5 = 0.8.
You want the P(x>0.8) for the beta distribution.
[tex]= \int_{0.8}^1 \frac{ ( \alpha + \beta -1)!}{(\alpha -1)! (\beta-1)!} x^{\alpha -1} (1-x)^{\beta-1} \\ \\ = 12 \int_{0.8}^1 x(1-x)^2 \\ \\ = 0.0272[/tex]
Answer: The probability it takes more than 2 days is 2.72%
