In this article, we will learn How to use the NORM.S.DIST function in Excel.
What is Normal Cumulative Distribution?
Normal Cumulative Distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is given by :
The value is basically called the Z value. The given mathematical formula to calculate is very complex. So, You can calculate the normal cumulative distribution of the given specific mean and standard deviation for the dataset using the NORM.DIST Function. Calculate the inverse of normal cumulative distribution using the NORM.INV Function.
Standard Normal Cumulative Distribution is a special case of the normal cumulative distribution with mean () = 0 and Standard deviation () = 1. The general form of Standard Normal Cumulative Distribution is given by :
You can calculate standard normal cumulative distribution using mean = 0 and standard deviation = 1 within NORM.DIST Function in Excel. The only variable the function relies on is the x value or else the z value.
Plot of Standard Normal distribution curve
The standard normal distribution has a mean of zero and a standard deviation of one. So, The probability density vs standard deviations curve for the standard normal cumulative distribution is shown below.
The mathematical formula stated above is very complex to intrep formula wise, so excel gave the default formula. Now let's learn how to calculate the standard normal probability for cumulative distribution or probability mass distribution using the NORM.S.DIST function in Excel.
NORM.S.DIST function in Excel
The function does the same work as the mathematical formula. The function takes the x or z value as an argument and a cumulative argument which defines the type of result pdf or cdf. Lets understand more about arguments below
NORM.S.DIST Function syntax:
x : value for which you want the distribution
cumulative : logical value that determines the form of the function. If cumulative is TRUE, NORM.S.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.
All of these might be confusing to understand. Let's understand how to use the function using an example. Here we take some x values and learn the different distribution types. First we will evaluate the cumulative distribution having z value 2 for standard normal distribution which has default mean = 0 and standard deviation = 1
Use the formula:
The probability value corresponding to 2 comes out to be
0.05 for the standard normal distribution dataset. Now extract probability for the probability mass distribution for the same z value as shown below.
Use the formula:
As you can see the probability for this is much higher than the previous value. You can inspect the both values for the different z values. Just copy the formula to other cells using the Ctrl + D shortcut key or dragging down from the right bottom of the cell.
As you can see the difference in results as shown in the image above. You noticed how much easy excel made the complex formula for you. You can get the same result using the NORM.DIST function with placing mean = 0 and standard deviation = 1. You can also find the inverse of the standard normal cumulative distribution using the NORM.S.INV function.
Here are all the observational notes using the NORM.S.DIST function in Excel
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