NORM.S.INV Function in Google Sheets

What Is NORM.S.INV Function in Google Sheets?

The NORMSINV function in Google Sheets is used to find the inverse of the standard normal cumulative distribution function (CDF). It has a single argument and takes a value between 0 and 1. It returns the corresponding z-score. For the uninitiated, the z-score in a standard normal distribution is the number of standard deviations a value is from the mean. We get the random variable’s value that corresponds to the specified cumulative probability.

It is one of the popular statistical functions offered by Google Sheets. In Google Sheets, NORM.S.INV and NORMSINV Google function are both used to return the inverse of the standard normal cumulative distribution for a given probability. NORM.S.INV is a more modern and recently used function while NORMSINV is older and supported for backward compatibility. In the example below, you must find the z-score that corresponds to the 94th percentile in the standard normal distribution. Apply the formula as shown.

=NORM.S.INV(0.94). You get a z-score of 1.554, which means that 94% of the data falls below this in a standard normal distribution.

Syntax

The NORM.S.INV function returns the inverse of the standard normal cumulative distribution. It is useful for finding the z-score corresponding to a given probability in a standard normal distribution. The following is the syntax for using NORM.S.INV:

=NORM.S.INV(probability)

Here, “probability” means the value you want to calculate in a standard normal distribution that should be between 0 and 1.

How to use NORM.S.INV Function in Google Sheets?

There are two ways to enter the NORM.S.INV function in Google Sheets.

Using the NORM.S.INV function in Google Sheets is very easy. Following are the steps.

Entering the NORM.S.INV Function manually

Step 1: Select an empty cell in your spreadsheet for the result.  Enter the details as shown below. Here, we will try to find the z-score for a probability of 0.90 or 90%. 

Step 2: Enter the NORM.S.INV formula by entering an equal’s sign – followed by a parenthesis.

Step 3: Inside the parentheses, specify the probability. Here, we specify the cell reference holding the probability, B1. Press Enter to apply the formula and display the result.

The result represents the inverse of the standard normal cumulative distribution associated with the specified probability.

Using the Google Menu bar

1.           Choose the cell where you want to enter the NORM.S.INV formula.

2.           Go to the menu bar and click on “Insert” – “Function” – “Statistical” – “NORM.S.INV”

3.           Enter the required argument. Close the bracket and press the “Enter” key.

Thus, the NORM.S.INV function in Google Sheets is useful in statistical analysis to find the value corresponding to a given probability in a standard normal distribution. It is very useful in finance, research, and quality control.

Examples

We can use the NORM.S.INV function in  Google Sheets in different ways such as to find the critical value for a given significance level, Find the z-score for a probability, etc. Let us look at some of the examples below to understand it better.

Example #1

We can use the NORM.S.INV function in  Google Sheets in different ways, such as finding the critical value for a given significance level, Finding the z-score for a probability, etc. Let us look at some of the examples below to understand it better.

Step 1: Enter the probability value in Google sheets.

Step 2: Enter the following formula in cell B2.

=NORM.S.INV(B1)

Step 3: Press Enter. The function will return approximately 1.88, which is the z-score. Using other values, such as the mean and standard deviation, you can use NORM.S.INV to set control limits in a quality control process.

Example #2

Suppose we have a data set with a mean value of 50 and a standard deviation of 10. We must find the value that corresponds to a probability of 0.93.

Step 1: Enter the details in the Google sheet as shown below.

Step 2: Now, use the following formula in B4 to find the value that corresponds to a probability of 0.93.

=50 + 10 * NORM.S.INV(0.93)

Step 3: Press Enter. We get 64.75 approximately,  which represents the value at which 93% of the data falls within the given mean and standard deviation.

Example #3

We can use the NORM.S.INV function in Google Sheets to analyze investment risk. For example, we calculate z-scores for different probabilities of loss in an investment.

Here our goal is to assess the risk of investment returns.

Step 1: Let us enter the probability of loss values in column A and find the Z-score in Column B.

Step 2: Let us now calculate the z-scores. In B2, enter the following formula and press Enter.

=NORM.S.INV(A2)

Step 3: Now, drag the formula till B5 and check the results.

Step 4: The z-scores indicate the thresholds for loss for the different percentages.

NORM.S.INV vs NORM.INV functions in Google Sheets

In Google Sheets, we observe two kinds of functions, NORM.S.INV and NORMSINV. The main difference between the two is that NORM.S.INV returns the inverse of the standard normal cumulative distribution, whereas NORM.INV returns the inverse of the normal cumulative distribution. Here, normal cumulative distribution describes the probability that a random variable is less than or equal to a certain value and has any mean or standard deviation. The standard normal cumulative distribution has a mean of 0 and a standard deviation of 1.

NORM.S.INV

1. It returns the inverse of the standard normal cumulative distribution for a given probability.
2. Its syntax is =NORM.S.INV(probability)
3. NORM.S.INV takes only one argument, which is the probability (a value between 0 and 1).
4. We use NORM.S.INV when specifically dealing with the standard normal distribution (mean = 0, standard deviation = 1).

NORM.INV

1. It returns the inverse of the normal cumulative distribution for a specified mean and standard deviation.
2. Its syntax is =NORM.INV(probability, mean, standard_deviation)
3. NORM.INV takes three arguments: probability, mean, and standard deviation.
4. We use the NORM.INV when finding the value for a normal distribution with a different mean and standard deviation.

Important Things to Note

1. NORM.S.INV helps identify abnormal data points in quality control by comparing them to the standard normal distribution which is very useful.
2. The mean of the distribution is 0 and the standard deviation is 1.
3. The output of the function is known as the z-score which corresponds to that cumulative probability. Suppose the probability is 97%, the output would be the z-score where 97% of the distribution lies below that score.
4. As the cumulative probability approaches one, the output approaches positive infinity.
5. The function is available in both Excel and Google Sheets.

Frequently Asked Questions (FAQs)

Download Template

This article must be helpful to understand the NORM.S.INV Function in Google Sheets, with its formula and examples. You can download the template here to use it instantly.

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