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Excel NORM.INV Function

The NORM.INV calculates and returns the inverse of the normal cumulative distribution for the given arithmetic mean and standard deviation.

norm.inv function 1


Syntax

=NORM.INV(probability, mean, standard_dev)


Arguments

  • probability (required): The probability corresponding to the normal distribution. It is the value at which you want to evaluate the inverse function.
  • mean (required): The arithmetic mean of the distribution.
  • standard_dev (required): The standard deviation of the distribution.

Return Value

The NORM.INV function returns a numeric value.


Function Notes

  • The #VALUE! error occurs if any of the supplied arguments is nonnumeric.
  • The #NUM! error occurs if:
    • standard_dev ≤ 0;
    • probability ≤ 0 or probability ≥ 1.

Example

norm.inv function 2

Suppose that you have a list of probabilities (normal cumulative distribution) that are calculated with the NORM.DIST function as shown in the formula bar above, to get the inverse of the cumulative distribution with the same set of mean and standard deviation values, please copy or enter the formula below in cell F9, and press Enter to get the result:

=NORM.INV(C9,$B$3,$B$6)

√ Note: The dollar signs ($) above indicate absolute references, which means the array argument in the formula won't change when you move or copy the formula to other cells. However, there are no dollar signs added to probability since you want it to be dynamic. After entering the formula, drag the fill handle down to apply the formula to the below cells.

norm.inv function 3

Note that for the normal cumulative distribution (probability) that is calculated with NORM.DIST(x, mean, standard_dev, TRUE), the NORM.INV function will return the x value based on the same probability, mean and standard_dev.


NORM.INV VS. NORM.S.INV

  • NORM.INV uses the normal distribution with the mean and standard deviation you specified;
  • NORM.S.INV uses the standard normal distribution which is a special case of the normal distribution where the mean is 0 and the standard deviation is 1.

Related functions

Excel NORM.S.INV Function

The NORM.S.INV calculates and returns the inverse of the standard normal cumulative distribution that has an arithmetic mean of 0 and standard deviation of 1 with a given probability.

Excel NORM.DIST Function

The NORM.DIST calculates and returns the cumulative distribution function or probability density function of a value for the given arithmetic mean and standard deviation.

Excel NORM.S.DIST Function

The NORM.S.DIST calculates and returns the standard normal cumulative distribution function or probability density function of a value for an arithmetic mean of 0 and standard deviation of 1.


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