Originally Posted by

**earachefl** Given a random variable x whose probability distribution is:

x = 0, P(x) = .03125

x = 1, P(x) = .15625

x = 2, P(x) = .3125

x = 3, P(x) = .3125

x = 4, P(x) = .15625

x = 5, P(X) = .03125

determine the probability that $\displaystyle (\mu - 2\sigma \leq x \leq \mu + 2\sigma)$.

I get $\displaystyle \mu = 2.5, \sigma \approx 1.118$, so the equation should be $\displaystyle P(.264 \leq x \leq 4.736)$ but I can't remember how to figure the probability from that! I know that the Empirical rule tells us that for a mound shaped distribution, the probability should be approx. .95, but how to figure it exactly?