# How to use the NORM.DIST function

**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**is the difference between an individual data point and the mean.**Standard deviation**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 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 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.DIST function Syntax

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

### NORM.DIST function Arguments

x |
Required. A numberÂ to calculate the distribution for. |

mean |
Required. The average of the distribution. |

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

cumulative |
Required. A boolean value that determines which distribution the NORM.DIST function returns. TRUE - Cumulative distribution FALSE - Probability mass function |

**What is the probability mass function?**

NORM.DIST with the cumulative parameter set to FALSE returns the value of the probability density function which is the value at the y-axis for a given x-axis value. The image above shows the y value 0.24197 for x-axis value -1.

NORM.DIST(-1,0,1,FALSE) returns approx. 0.24197

NORM.DIST(-1,0,1,TRUE) returns approx.Â .15866 which is the integral from negative infinity to -1

The image above shows the integral from negative infinity to x axis value -1.

### NORM.DIST function example

Formula in cell C7:

If mean = 0, standard_dev = 1, and cumulative = TRUE, the standard normal distribution is returned.

If cumulative = TRUE, the formula is calculated the integral from negative infinity to x.

### NORM.DIST function not working

The NORM.DIST returns a

- #VALUE! error value if the
*mean*or*standard_dev*is nonnumeric. - #NUM! error value if
*standard_dev*â‰¤ 0

### How is the NORM.DIST function calculated?

The NORM.DIST function is very useful if you are working with statistics. Here is how the function works in detail (cumulative = FALSE).

*Âµ*Â is the mean.

*Ïƒ* is the standard deviation.

Use the AVERAGE function to calculate the arithmetic mean, used in the second argument in the NORM.DIST function.

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### 'NORM.DIST' function examples

The following article has a formula that contains the NORM.DIST function.

Table of Contents How to graph a normal distribution How to build an arrow chart How to graph an equation […]

### Functions in 'Statistical' category

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

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