Suppose X is normally distributed with variance σ2 = 16, and that P(X < 30) = 0.8413. The mean μ of X is

The mean is 26.  With the standard deviation = 4  we have:

 

\(\frac{1}{\sqrt{2\pi}\times 4}\int_{-\infty}^{30}e^{-\frac{1}{2}(\frac{x-26}{4})^2}dx=0.8413\)