Normal distribution, how to calculate $\mu$ and $\sigma$

Question

How to calculate $\mu$ and $\sigma^2$ when it is known just that $P(X\le 49)=0.6915$ and $P(X>51)=0.2266$ ?

Thank you very much!

Answer 1

Just quickly, using Mathematica :

Answer 2

I would say just the standard normal distribution table $P(U\le u) = \Phi(u)$:

$\frac{49-\mu}{\sigma}=\Phi^{-1}(0.6915)=0.5$

$\frac{51-\mu}{\sigma}=\Phi^{-1}(1-0.2266)=0.75$

Solving this system of equations: $\,\,\mu = 45,\,\,\sigma=8$.