A normally distributed random variable $x$ is known to satisfy $P(x>58)=0.24$ and $P(x>24)=0.87$. Determine the mean and variance which describe the distribution of $x$.
So I'm familiar with finding the variance and mean of probability density functions when I have an actual function to work with, but now that I'm working with just probabilities, all I've really been able to do with this is find the probability that $(x<24)=0.13$, probability $(24<x<58)=0.63$ and $P(x>58)$.
Would anyone be able to point me in the right direction, as I can't find a similar question in my lectures/course notes or online, they all seem to be done with functions.