# NORM.DIST

The NORM.DIST function calculates the probability that a value falls within a given range in a normal distribution. It is commonly used in statistics and probability analysis to determine the likelihood of a specific outcome occurring based on a normal distribution of data.

## Syntax

=NORM.DIST(`x`

, `mean`

, `standard_dev`

, `cumulative`

)

`x` | The value for which you want to calculate the probability in the normal distribution. | ||

`mean` | The arithmetic mean of the distribution. | ||

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

`cumulative` | A logical value that determines the form of the function. If TRUE | returns the cumulative distribution function; if FALSE | returns the probability density function. |

## About NORM.DIST

If you're delving into statistical analysis or probability assessments in Excel, NORM.DIST is your go-to function for estimating the likelihood of a value falling within a specified range in a normal distribution. This function can aid in making informed decisions based on the expected distribution of data points and their variability around the mean value. Understanding the probabilities associated with different outcomes can be crucial in fields such as finance, quality control, and scientific research, where uncertainty plays a significant role in decision-making processes. By leveraging NORM.DIST, you can gain insights into the probability of events occurring within the bounds set by the mean and standard deviation of the data.

## Examples

Suppose you have a normal distribution with a mean of 50 and a standard deviation of 10. You want to find the probability of a value being less than 45. The NORM.DIST formula would be:

=NORM.DIST(45, 50, 10, TRUE)

This will return the cumulative probability of a value less than 45 in the specified normal distribution.

If you aim to determine the probability density function for a value of 60 in the same distribution as above, the NORM.DIST formula would be:

=NORM.DIST(60, 50, 10, FALSE)

This will provide the probability density at the value of 60 within the distribution.

## Notes

Ensure that you input valid values for the mean and standard deviation that accurately represent the normal distribution of your data. The cumulative argument should be either TRUE or FALSE to specify whether you want the cumulative distribution function or the probability density function. Double-check your inputs to avoid errors in probability calculations.

## Questions

**How does the NORM.DIST function differ when the 'cumulative' argument is TRUE or FALSE?**

When the 'cumulative' argument is set to TRUE, NORM.DIST returns the cumulative distribution function (the probability of a value being less than or equal to the specified value). Conversely, when set to FALSE, it returns the probability density function (the likelihood of the value occurring at the specific point).

**Can the NORM.DIST function handle non-normal distributions?**

While NORM.DIST is specifically designed for normal distributions, it can still provide insights for distributions that exhibit some characteristics of normality. However, for highly skewed or non-normal distributions, other statistical functions may be more appropriate for accurate probability calculations.

**How should I interpret the output of the NORM.DIST function in real-world scenarios?**

The output of the NORM.DIST function represents the probability or likelihood associated with a particular value or range within a normal distribution. In practical terms, it can help in decision-making by quantifying the chance of certain events occurring based on the distribution's characteristics.

## Related functions

NORM.INV

NORM.S.DIST

NORM.S.INV

NORM.DIST.RT

NORM.INV.RT

NORM.INV.V

NORM.V

NORMDIST

NORMINV