Norm.Dist Google Sheets Function

What Is Norm.Dist Google Sheets Function?

Normal distribution curves are used in statistics to model real-world data. We have a statistical function NORM.DIST Google Sheets Function calculates the normal probability density function (PDF) and the normal cumulative distribution function (CDF) for a value.

For example, for a mean value of 20 and a standard deviation of 5, let us find the cumulative probability up to a certain value of x, which is 25, using the NORM.DIST function. Here, we set the cumulative argument to TRUE as it returns the cumulative distribution function (CDF). Hence, type the following formula in cell B5.

=NORM.DIST(B3,B1,B2,B4). Press Enter.

We get an output of 0.841. On the bell curve, it represents the area to the left of 25, which is approximately 84.1%.

Normal Distribution – CDF and PDF

For the uninitiated, in a normal distribution, most of the data points cluster toward the center of the range, and a lesser number gradually taper off symmetrically toward each extreme. One commonly uses this distribution in math and science.

The probability density function shows the probability that a continuous random variable takes a specific value. Also called PDF,  we can draw a graph with the area under the curve indicating the interval where the variable may occur. The cumulative distribution function or CDF shows the probability that a variable is less than or equal to a specified value.

Syntax

Here’s the syntax of the NORM.DIST Google Sheet function.

=NORM.DIST(x, mean, standard_deviation, cumulative)

Arguments:

1. x: The value for which you must calculate the distribution.
2. mean: The mean of the normal distribution.
3. standard_deviation: The standard deviation of the normal distribution.
4. cumulative: A logical value that determines the  distribution we want to use. If TRUE, it returns the cumulative distribution function (CDF). If FALSE, it returns the probability density function (PDF).

How To Use NORM.DIST Google Sheets Function?

We can use the NORM.DIST Google Sheets function in two ways.

These include:

1. Entering the NORM.DIST Google Sheet function manually.
2. Entering through the Google Menu Bar

Entering NORM.DIST Google Sheets Function Mnually

Let us take a simple example for applying the function manually. Let us calculate the probability that a value in a normal distribution that has a mean of 10 and a standard deviation of 3 is less than or equal to 7.

Step 1: We have to calculate the CDF here. First, enter the details in the Google Sheet.

Step 2: Then, enter the below formula in cell B5.

=NORM.DIST(

B1,B2,B3,B4). Press Enter.

Step 3: Enter the arguments in the order shown below. Press Enter. You get the value of the normal CDF in cell C5.

Hence, the probability that the value x is less than or equal to 7 is 15.5%.

Step 5: Now, to get the value of the PDF, or the probability density at the value 7, let us make the fourth argument FALSE. Enter the following formula in cell B6.

=NORM.DIST(B1,B2,B3,FALSE)

Step 6: Press Enter. You get the result in cell B6, as shown.

Explanation: The cumulative distribution function in B5 shows the probability that x is less than or equal to 15.8%. In contrast, the normal probability density function shows that the probability that x is exactly 7 is 8.06%.

Entering NORM.DIST values through the Google Menu bar

You can also use the Norm.Dist Google Sheets function shortcut through the menu bar.

Step 1: Place the cursor where you want to enter the formula. Then, go to Insert – Function – Statistical – NORM.DIST. Select it, type in the required arguments, and close the braces. Press Enter to get the result.

Examples

Let us look at some examples below.

Example #1

Let us look at an example of some values given in a column. We have a mean of 54 entered in cell E3 and SD of 22 in cell E4. Let us calculate the CDF.

Step 1: We can find the CDF value for the different values in Column A using the function shown below. Here, we enter the mean and SD values in cells E3 and E4.

Enter the formula in cell B1.

=NORM.DIST(A1,E3,E4,TRUE).

The above formula is entered, and then Press Enter. You get the result shown below.

Step 2: Since the mean and SD values are fixed, let us use those cells as absolute references.

Step 3: Copy the following formula in the image into cell B2 and drag the Autofill handle from cell B2 to B5. You get the CDF values for values in Column A.

Thus, the NORM.DIST function helps calculate the CDF values in many cases.

Example #2

In the above example, we calculated the CDF by keeping argument 4 as TRUE. In this Norm.DIST Google Sheets function example, let us calculate the clothes sizes of all females in a particular locality who are normally distributed with a mean value of size 38. The standard deviation is 2. If you want to calculate the percentage of females with an exact dress size of 42, you can do it the following way.

Step 1: Enter the formula to calculate the normal probability density function for a value 42 in cell A2, as shown below.

Step 2: Press Enter.You get a result of 0.0044 in cell A1, which indicates that the percentage of women with a dress size 42 for the above parameters stands at 2.69%%.

Thus, we obtain the the probability density value using the NORM.DIST function, which substitutes the fourth argument with the value 0/FALSE.

Example #3 – NORMDIST Array-Formula Use in Google Sheets

We can also use NORM.DIST with ARRAYFORMULA to work on the entire array of names simultaneously. Let us enter some values in Column A.

Let the mean be 60 and SD, 10.Let the mean be 60 and SD, 10.

Step 1: Now, obtain the CPF value using the NORM.DIST Google Sheets function. Go to cell D1 and enter the following formula using absolute references for the mean and SD. 

=NORM.DIST(A1,$C$1,$C$2,FALSE)

However, we need the result for all the values in Column A simultaneously. Wrap the above formula with the function ARRAYFORMULA.

Step 2: Press Enter. You get the CDF for the entire Column A at once.

Norm.Dist vs. Norm.Inv in Google Sheets

The Norm.Dist and Norm.Inv functions are used as follows.

NORM.DIST

1. Norm.Dist is used when you want to find the probability of finding a value less than or equal to X. It is very useful to find the probability of finding a value more than or equal to X using the formula: 1 – Norm.Dist.
2. To summarize, it Computes the probability for a given value (x) in a normal distribution
3. The syntax for NORM.DIST is as follows: =NORM.DIST(X, mean, standard deviation, cumulative). It returns probability (‘p’) or the area under the normal curve to the left of a value X.

NORM.INV

1. Norm.Inv is used when you are given the probability and want to find the value of X for it.
2. NORM.INV(p, mean, standard deviation, cumulative) returns the value x, which has a probability of p or the area under the normal curve N to the left.
3. To summarize, it Computes the value (x) given a probability in a normal distribution.

A clear example that indicates the difference is as follows.

For instance, we have 200 apples, which means we have a standard deviation of 30 apples. To find the probability of the demand for apples being less than 150 on a particular day, we use the function NORM.DIST with x = 150. Suppose there is a 40% chance that all the apples will be sold away; what is the value of x that should be stocked so that there are enough apples? Here, we use NORM.INV.

Important Points To Remember

1. The CDF returns the area to the left of the x value mentioned under the bell curve.
2. The PDF returns the value on the points on the curve.
3. The #NUM error occurs when the standard deviation value entered as the third argument is less than or equal to zero.
4. In a normal distribution, most of the data points cluster toward the center of the range, and a lesser number of data points gradually taper off symmetrically toward each extreme

Frequently Asked Questions (FAQs)

Download Template

This article must help understand the Norm.Dist Google Sheets Function, with its formula and examples. You can download the template here to use it instantly.

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