If a certain normal distribution of $X$, the probability is $0.5$ that $X$ is less than $500$ and $0.0227$ that $X$ is greater than $650$. What is the standard deviation of $X$?
For finding S.D. we need mean but its not given.
Please explain how to approach this question.
From the fact that $\mathbb{P}(X<500)=\frac{1}{2}$ we have that $\mathbb{E}[X]=500$ due to the symmetry of the normal distribution. Now continue with your approach