Here is my homework problem. Again, sorry for the formatting:
A continuous random variable $X$ has a symmetric distribution with mean $18$. A brilliant mathematician has estimated that the probability that $X$ is less than $12$ is at most $12.5 %$. Approximate the probability that $X$ lies between $7$ and $29$. Giant hint: what is the standard deviation?
So far I have determined that:
$mean=\mu=18$
$p(x \lt 12)\le0.125$
I know that
Standard Deviation= $\sigma= \sqrt{\text{Variance of x}}$
and that $Var(x) = E(x^2)-\mu^2 =\int_a^b x^2 f(x)dx$
Because it has symmetric distribution I feel like I should be able to determine $E(x^2)$ without knowing $f(x)$. But I have nothing in my notes as to how to accomplish this. Can anyone point me in the right direction?