Inverse Cumulative Standard Normal Probability Calculator


Instructions: Compute the inverse cumulative score for the standard normal probability distribution. Provide a cumulative probability \(p\) (a value on the interval [0, 1]), and the solver will find the z-value \(z\) so that \(\Pr(Z \le z) = p\).

Cumulative Probability (\(p\))

More about this Inverse Cumulative Standard Normal Probability Calculator

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

Example: Assume that \(Z\) has a standard normal distribution variable. Let us assume we want to compute the \(z\) score so that the cumulative normal probability distribution is 0.89. 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. Follow this link to compute normal probabilities

For a more general normal distribution, you can use this cumulative distribution grapher for generic normal distributions to instead compute cumulative values.




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