# NORMDIST Function

Get the normal distribution for a stated mean and standard distribution

Get the normal distribution for a stated mean and standard distribution

The NORMDIST Excel function is categorized under Statistical functions and will return the normal distribution for a stated mean and standard distribution. That is, it will calculate the normal probability density function or the cumulative normal distribution function for a given set of parameters.

To understand what a normal distribution is, let us consider an example. Suppose we take an average 30 minutes to commute to the office daily, with a standard deviation of 5 minutes. Assuming a normal distribution for the time it takes to go to work, we can calculate the percentage of time for which the commuting time would be between 25 minutes and 35 minutes.

As a financial analyst, the NORMDIST function is useful in stock market analysis. While investing, we need to balance between risk and return and aim for the highest possible return. Normal distribution helps quantify the amount of return and risk by the mean for return and standard deviation for risk.

**=NORMDIST(x,mean,standard_dev,cumulative)**

The NORMDIST function uses the following arguments:

**X**(required argument) – It the value for which we wish to calculate the distribution.**Mean**(required argument) – It is the arithmetic mean of the distribution.**Standard_dev**(required argument) – It is the standard deviation of the distribution.**Cumulative**(required argument) – It is a logical value. It specifies the type of distribution to be used: TRUE (Cumulative Normal Distribution Function) and FALSE (Normal Probability Density Function).

The formula used for calculating the normal distribution is:

Where:

*μ*is the mean of the distribution*σ*is the variance, and^{2 }*x*is the independent variable for which you want to evaluate the function- The Cumulative Normal Distribution function is given by the integral, from
*-∞*to*x*, of the Normal Probability Density function.

To understand the uses of the NORMDIST function, let us consider an example:

Suppose we are given the following data:

- Value for which we need distribution:
**52** - Arithmetic mean of the distribution:
**50** - Standard deviation of the distribution:
**2.5**

If we wish to calculate the cumulative distribution function for the data above, the formula to use is:

We get the result below:

If we wish to calculate the probability mass function for the data above, the formula to use is:

We get the result below:

- The NORMDIST function was replaced by NORM.DIST function in Excel 2010. NORM.DIST provides more accuracy than the NORMDIST function. The NORMDIST function is still available in Excel 2010 version. However, it is stored in the list of compatibility functions to allow compatibility with earlier versions of Excel.
- The NORM.DIST function refers to any normal distribution, whereas the NORMSDIST compatibility function and the NORM.S.DIST function refers specifically to the unit normal distribution.
- #NUM! error – Occurs if the given standard_dev argument is less than or equal to zero.
- #VALUE! error – Occurs when any of the given argument is non-numeric or is a non-logical value.
- If mean = 0, standard_dev = 1, and cumulative = TRUE, NORMDIST returns the standard normal distribution, NORMSDIST.

**Click here to download the sample Excel file**

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