# How to use the NORM.INV function

**What is the NORM.INV function?**

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

**What is the NORM.DIST function?**

The NORM.DIST function calculates the normal distribution for a given mean and standard deviation.

**What is a normal distribution?**

The normal distribution is a symmetric bell-shaped probability distribution described by its mean and standard deviation. Used by many to model a plethora of natural phenomena and represent unknown processes.

**What is the mean?**

It is also known as the average. It is calculated by adding up all the values in the data set and dividing by the number of values.

For example, if you have a data set of 5, 7, 9, 11, and 13, the mean is (5 + 7 + 9 + 11 + 13) / 5 = 9.

**What is deviation?**

In statistics, deviation is a measure of how far each value in a data set lies from the mean (the average of all values). A high deviation means that the values are spread out widely, while a low deviation means that they are clustered closely around the mean.

**What is standard deviation?**

Standard deviation measures dispersion from the mean by taking the square root of the average of squared deviations, useful for assessing variability and spread in data.

**What is the difference between deviation and standard deviation?**

**Deviation**Â is the difference between an individual data point and the mean.**Standard deviation**Â measures the variation across all deviations by using the square root of the average squared deviation.

**What is the difference between the NORM.DIST function vs NORM.INV function?**

NORM.INV function returns the inverse of the normal cumulative distribution for a given mean and standard deviation.

NORM.INV(*probability*,Â *mean*,Â *standard_dev*)

The NORM.DIST function calculates the normal distribution for a given mean and standard deviation.

NORM.DIST(*x,Â mean,Â standard_dev,Â cumulative)*

For example, the chart above demonstrates a standard normal distribution with a mean of 0 (zero) and standard deviation of 1.

The NORM.DIST(-1,0,1,TRUE) returns 0.158655253931457 which is the orange area below the curve up to x = -1 that represents the cumulative probability.

The NORM.INV(0.158655253931457,0,1) returns -1 which is the x value given the cumulative probability of 0.158655253931457

**What is a standard normal distribution?**

A standard normal distribution is a normal distribution with the mean of 0 (zero) and the standard deviation is 1. You can standardize any normal distribution using the STANDARDIZE function in Excel, it works like this:

z = (x - *Âµ)/Ïƒ*

*z = z-score
Âµ*Â is the mean.

*Ïƒ*Â is the standard deviation.

### NORM.INV function Syntax

NORM.INV(*probability*,Â *mean*,Â *standard_dev*)

### NORM.INV function Arguments

probability |
Required. A probability corresponding to the normal distribution. |

mean |
Required. The average of the distribution. |

standard_dev |
Required. The standard deviation of the distribution. |

### NORM.INV function example

Formula in cell C7:

### NORM.INV function not working

NORM.INV returns

- #VALUE! if argument is non-numeric.
- #NUM! if standard_dev â‰¤ 0
- #NUM! if probability <= 0 or if probability >= 1
- the standard normal distribution if mean = 0 and standard_dev = 1

### Functions in 'Statistical' category

The NORM.INV function function is one of 74 functions in the 'Statistical' category.

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