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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!
$\endgroup$ 12 Answers
$\begingroup$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: $\,\,\mu = 45,\,\,\sigma=8$.
$\endgroup$ $\begingroup$Just quickly, using Mathematica :
