# NORM.INV Excel

## What Is NORM.INV Excel?

NORM.INV in Excel is a statistical function used to calculate the inverse of the normal distribution for a specified mean and SD. It allows users to determine the threshold value at which a given percentage of data falls below the value in a normally distributed dataset. This function is handy in analyzing and interpreting data, especially in fields such as finance, engineering, and insurance, where understanding probabilities by utilizing NORM is crucial.

The Excel function helps in performing hypothesis testing, generating statistical models, and predicting outcomes with greater accuracy. With its robust capabilities for handling complex calculations involving normal distributions and probabilities, NORM.INV is an essential tool for professionals looking to gain insights from their data and improve decision-making processes.

The NORM.INV function can be used to find a specific value in a normal distribution. In this example, the formula =NORM.INV(B3,B1,B2 is entered in cell B4, and the result is calculated.

### Syntax

Probability – This is a required argument. It represents the probability associated with the normal distribution. It denotes the value at which we intend to evaluate the inverse function.

Mean – This is a required argument. It signifies the arithmetic mean of the distribution.

Standard_dev -This is the required argument. It indicates the standard deviation of the distribution.

###### Key Takeaways
• The Excel NORM.INV function is used to calculate the inverse of the Cumulative Normal Distribution Function. It requires a probability value, distribution mean, and a standard deviation as inputs.
• This function was introduced in Excel 2010. However, it is essentially an updated version of the NORMINV function, which can be used in older versions of Excel.
• The NORM.INV Excel function can provide estimates for non-normal data, but caution should be exercised in interpreting and relying on its results without considering the potential limitations imposed by deviations from normality.

### How To Use NORM.INV Function in Excel?

To effectively utilize the NORM.INV function Excel, follow these steps.

#### #1 – Access from the Excel ribbon

Step 1: Choose the empty cell which will contain the result. Go to the “Formulas” tab and click it.

Step 2: Select the “More Functions” option from the menu.

Step 3: Select the “Statistical” option from the drop-down list. Select “NORM.INV” from the drop-down menu.

Step 4: A window called “Function Arguments” appears. As the number of arguments, enter the value in the “probability,” “mean” and “standard_dev.”

Select OK.

#### #2 – Enter the worksheet manually

Step 1: Select an empty cell for the output. Type “=NORM.INV()” in the selected cell. Alternatively, type “=N” and double-click the NORM.INV function from the list of suggestions shown by Excel.

Step 2: Press the “Enter” key to get the result.

### Examples

#### Example #1 – Using Cell References

To better understand and apply the concept of the NORM.INV Excel function using cell references, let’s consider the following example. In the provided table, the data is organized as follows:

To calculate the desired output in cell B4, please follow these steps.

Step 1: Select the cell where the formula will be entered, and the result will be calculated. For this demonstration, let’s choose cell B4. Enter the formula. The complete formula to be entered in cell B4 is:

=NORM.INV(B3,B1,B2).

Step 2: After entering each value in the previous step, press the Enter key. The resulting value will be displayed in cell B4, as shown in the provided image.

#### Example #2 – Analyzing Test Scores

To gain a comprehensive understanding, there are the scores of 5 students in class, and we will effectively apply the NORM.INV Excel function utilizing analyzing their test scores. Here, we will find the range of values of the lowest 75% of the scores.

Within the given table, the data is structured as follows:

• Row 1 encompasses the mean of the scores.
• Row 2 encompasses their standard deviation.
• Row 3 encompasses the probability value, which is 0.75, as we are calculating for a threshold of 75%
• Row 4 encompasses the result.

Step 1: Let us calculate the mean scores using the formula =AVERAGE(B1:F1). Enter the above formula in cell B2.

Step 2: To calculate the standard deviation using STDEV excel function, input the formula =STDEV(B1:F1) in cell B3.

Step 3: After entering the value 0.75 in cell B4, let us add the formula =NORM.INV(B4,B2,B3) in B5. You will get a result of 85.11

It means that scores that are less than or equal to 85~ comprise the bottom 75% of the scores. It is beneficial in identifying students based on their performance.

#### Example #3 – Evaluating Investments

The NORM.INV Excel function can be used to evaluate the risk and return of various investments. We can use the function NORM.INV to calculate the return on an investment. Let’s delve into the following example:

The given table is structured as follows:

• Row 1 represents the mean on the returns of an investment.
• Row 2 represents the standard deviation.
• Row 3 represents the percentage for which we will evaluate the return value. It is 10% here as it represents a common measure of downside risk.
• Row 4 is used to obtain the result of the z-score(number of SDs from the mean of a distribution) corresponding to 10%.

Step 1: Choose the cell where the formula will be inserted, and the result will be computed. For this demonstration, let’s select cell B4. Now input the following formula here.

=NORM.INV(B3/100, B1, B2).

Here, B3/100 is the probability, the mean is 0.08, and the SD is 0.02

Step 2: Press Enter to get the investment return value below, which is just 10% of the expected returns.

Thus, using the NORM.INV function we can assess the downside risk of the investment.

### NORM.INV Excel vs NORM.S.INV Excel

NORM.INV and NORM.S.INV are two Excel functions used for calculating the inverse of the standard normal cumulative distribution.

The main difference between these functions lies in their inputs and outputs.

• NORM.INV Excel function requires a probability value (between 0 and 1) as its first argument, representing the area under the curve and returning the corresponding z-score or standard deviation.

On the other hand, NORM.S.INV takes a probability value as its only argument but assumes a standard normal distribution with a mean of zero and a standard deviation of one. Consequently, it provides an output value without considering any additional factors.

• The data that has a known mean and standard deviation, such as in finance or statistics applications, NORM.INV may be more suitable to incorporate these parameters into the calculation.

However, if you already have standardized data, NORM.S.INV can simplify your analysis by assuming certain parameters automatically.

### Important Things To Note

• When the mean is equal to zero, and the standard deviation is equal to 1, the NORM.INV Excel function utilizes the standard normal distribution.
• An error labeled as #VALUE! may occur if any of the provided arguments are non-numeric.
• An error labeled as #NUM! may occur in the following situations:
• If the given probability argument is less than zero or greater than one.
• If the given standard_dev argument is less than or equal to zero.

1. Does the NORM.INV function handles non-normal distributions as well.

The NORM.INV Excel function, also known as the inverse normal distribution function, is predominantly used to calculate the value of a standard normal variable given a probability. While it is specifically designed for normally distributed data, it can still handle non-normal distributions effectively when certain conditions are met. However, it is important to note that the accuracy and reliability of results obtained from NORM.INV with non-normal distributions may be compromised. In such cases, alternative methods like transformation or approximation techniques may yield more accurate outcomes. It is also worth mentioning that specialized functions exist for specific non-normal distributions such as lognormal or Weibull distributions.

2. Are there any limitations or constraints when using the NORM.INV function in Excel?

There are indeed limitations and constraints when using the NORM.INV function in Excel.
• It is crucial to note that this function assumes a normal distribution of the data being analyzed. Therefore, if the underlying data does not follow a bell curve pattern, the results are obtained from NORM.INV Excel may not accurately reflect reality.
• Additionally, this function relies on certain assumptions such as independence of observations and constant variance. Violating these assumptions can significantly impact the validity of the results obtained.
• Furthermore, it is essential to exercise caution with extreme input values or when extrapolating beyond the range of observed data since NORM.INV may lead to unreliable or nonsensical outcomes in such cases.
• Lastly, understanding how to interpret and utilize the output from NORM.INV is equally important, as misinterpretations can lead to erroneous conclusions or inappropriate decision-making processes.

3. Where is the NORM.INV function in the Excel sheet?

One can activate the NORM.INV function in Excel using the following steps:
• Choose the empty cell which will contain the result.
• Go to the “Formulas” tab and click it.
• Select the “Statistical” group.
• Select “NORM.INV” from the drop-down menu.
• A window called “Function Arguments” appears.
• As the number of arguments, enter the value in the “probability,” “mean” and “standard_dev.”
• Select OK.