# Inverse Cumulative Normal Probability Calculator

Instructions: Compute the inverse cumulative normal probability score for a given cumulative probability. Give a cumulative probability $$p$$ (a value on the interval [0, 1]), specify the mean ($$\mu$$) and standard deviation ($$\sigma$$) for the variable $$X$$, and the solver will find the value $$x$$ so that $$\Pr(X \le x) = p$$. Pop. Mean ($$\mu$$) Pop. St. Deviation ($$\sigma$$) Cumulative Probability ($$p$$)

This Inverse Cumulative Normal Probability Calculator will compute for you a score $$x$$ so that the cumulative normal probability is equal to a certain given value $$p$$. Mathematically, we find $$x$$ so that $$\Pr(X \le x) = p$$.

Example: Assume that $$X$$ is a normally distributed variable, with mean $$\mu = 500$$ and population standard deviation $$\sigma = 100$$. Let us assume we want to compute the $$x$$ score so that the cumulative normal probability distribution is 0.89. First, the z-score associated to a cumulative probability of 0.89 is

$z_c = \Phi^{-1}(0.89) = 1.227$

This value of $$z_c = 1.227$$ can be found with Excel, or with a normal distribution table. Hence, the X score associated with the 0.89 cumulative probability is

$x = \mu + z_c \times \sigma = 500 + 1.227 \times 100 = 622.7$

### The Standard Normal Distribution

If you are dealing specifically with the standard normal distribution, you could check this Inverse Cumulative Standard Normal Probability Calculator.

Other graph creators that you could use are our normal probability plot, normal distribution grapher or our Pareto chart marker.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us. 