NORMINV

Syntax: NORMINV(P, M, S)

P = a numeric probability (0 < P < 1)
M = the mean of the normal distribution
S = the standard deviation of the normal distribution

The inverse of the cumulative normal distribution function. NORMINV returns the value X such that the integral from minus infinity to X of the normal distribution function with mean M and standard deviation S is equal to P. P must be greater than 0 and less than 1, and S must be greater than 0.

The mathematical formulation is given by:

$$\mbox{{\it X}, such that} \; P = \int_{-\infty}^{X} \frac{1}{\sqrt{2\pi \times S}} e^{-\frac{(t-M)^2}{2S^2}} dt$$

Examples:

NORMINV(0.5, 0, 1) = 0

NORMINV(0.975, 0, 1) = 1.959964

NORMINV(NORMDIST(0.88, 0, 1, 1), 0, 1) = 0.88

NORMINV(1, 0, 1) = Error

Excel function: NORMINV