# NORM.INV Function

Calculate the inverse of the normal cumulative distribution for a given value of x

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## What is the NORM.INV Function?

The NORM.INV Function[1] is categorized under Excel Statistical functions. It will calculate the inverse of the normal cumulative distribution for a supplied value of x, with a given distribution mean and standard deviation. The function will calculate the probability to the left of any particular point in a normal distribution.

For example, suppose we are given a normally distributed random variable that is denoted by x. For the value of x, if we wish to get the bottom 5% of the distribution, we can use the NORM.INV function.

As a financial analyst, the function is useful in stock market analysis. We can use NORM.INV to understand how a portfolio is affected by any additions or withdrawals made.

### Formula

=NORM.INV(probability,mean,standard_dev)

The NORM.INV formula uses the following arguments:

1. Probability (required argument) – This is the probability corresponding to normal distribution. It is the value at which we want to evaluate the inverse function.
2. Mean (required argument) – This is the arithmetic mean of the distribution.
3. Standard_dev (required argument) – This is the standard deviation of the distribution.

The normal distribution is a continuous probability function and is given by the formula:

Where:

• μ is the mean of the distribution
• σis the variance
• is the independent variable for which you want to evaluate the function

### How to use the NORM.INV Function in Excel?

The NORM.INV function was introduced in Excel 2010. To understand the uses of the function, let’s consider an example:

#### Example

Suppose we are given the following data:

• Probability: 0.56
• Arithmetic mean of the distribution: 5
• Standard deviation of the distribution: 2

If we wish to calculate the value of the function, the formula to use will be:

We get the result below:

### Notes about the NORM.INV Function

1. If the mean equals zero and the standard deviation equals 1, NORM.INV uses the standard normal distribution.
2. #VALUE! error – Occurs if any of the given arguments is non-numeric.
3. #NUM! error – Occurs when:
• The given probability argument is less than zero or greater than one.
• The given standard_dev argument is less than or equal to zero.