If i have a beta distribution with (alpha = beta = 2) then i know that the mean is 0.5 and the variance is 0.05, with SD = 0.224(3dp) from the standard rules. I am trying to find the probability that a random variable x lies within 2 SD's of the mean. so far i have got

Pr(mean - 2Sd's < x < mean + 2Sd's)

=Pr (0.052 < x < 0.948)

anyone got any ideas how to find the probability from here.

Thanks for any help.

Tom