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:
I know that Standard Deviation= σ= Square Root of Variance of x
and that Var(x) = E(x^2)-μ^2 = integral from a to b of 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?