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 (\(p\))

More about this Inverse Cumulative Normal Probability Calculator

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

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



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