# NORM.S.DIST

The NORM.S.DIST function in Excel calculates the standard normal cumulative distribution function for a specified value. It is commonly used in statistical analysis and probability calculations to determine the probability of a value being less than or equal to a given standard normal random variable.

## Syntax

=NORM.S.DIST(`Z`

, `Cumulative`

)

`Z` | The value for which you want to calculate the standard normal cumulative distribution. |

`Cumulative` | A logical value that specifies the form of the function. TRUE returns the cumulative distribution function; FALSE returns the probability density function. |

## About NORM.S.DIST

When you're delving into statistics and need to assess the likelihood of a certain event occurring based on a standard normal distribution, NORM.S.DIST comes to your aid in Excel. This versatile function provides valuable insights by calculating the probability of a value falling below a specified standard normal random variable Z. By utilizing the standard normal distribution (mean of 0 and standard deviation of 1), NORM.S.DIST simplifies the process of determining the probability associated with Z in statistical analyses and risk assessments. You have the flexibility to obtain either the cumulative distribution function or the probability density function by setting the Cumulative argument accordingly.

## Examples

Suppose you want to find the probability that a standard normal random variable Z is less than or equal to 1.5. The NORM.S.DIST formula would be: =NORM.S.DIST(1.5, TRUE)

If you seek to calculate the probability density of a standard normal random variable Z at 0.75, use the following formula: =NORM.S.DIST(0.75, FALSE)

## Notes

Ensure that the Z value provided aligns with a standard normal distribution, where the mean is 0 and the standard deviation is 1. The Cumulative argument should be set to TRUE for the cumulative distribution function or FALSE for the probability density function. Use Excel's precision functions to format the output to the desired accuracy level.

## Questions

**What does the Cumulative argument in the NORM.S.DIST function signify?**

The Cumulative argument in the NORM.S.DIST function determines the form of the function's output. When set to TRUE, it returns the cumulative distribution function (the probability that a random variable is less than or equal to a specific value). When set to FALSE, it returns the probability density function (the likelihood of the random variable taking on a particular value).

**Can the NORM.S.DIST function handle values outside the standard normal distribution parameters?**

The NORM.S.DIST function is specifically designed for standard normal distributions with a mean of 0 and a standard deviation of 1. It may not provide accurate results for values significantly deviating from this standard. Ensure the Z value reflects the constraints of the standard normal distribution for precise calculations.

**How can I interpret the output of the NORM.S.DIST function?**

The output of the NORM.S.DIST function represents the probability associated with a standard normal random variable Z. If you're using the cumulative distribution function, the result denotes the probability that a random variable is less than or equal to the specified Z value. For the probability density function, the output indicates the likelihood of the random variable attaining the particular Z value.