In this article, we will learn How to use the NORM.S.INV 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 NORMDIST 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 NORMDIST Function in Excel but Inverse of the standard normal distribution computes the critical value so that the cumulative distribution is greater than or equal to a pre-specified probability value (x). Learn how to calculate the inverse of standard Normal Cumulative Distribution in Excel using the NORM.S.INV function. That is, it returns the inverse of Z value, given the cumulative probability.
The standard normal distribution has a mean of zero and a standard deviation of one. The probability density vs standard deviations curve for the standard normal cumulative distribution is given below.
NORM.S.INV Function in Excel
NORM.S.INV function returns the inverse of the standard normal cumulative distribution for the dataset. The function only takes one argument, the probability value of the dataset.
NORM.S.INV Function syntax:
probability : probability value for the distribution dataset
All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have a dataset first we calculate the probability for the dataset and then we will calculate the inverse of the normal cumulative distribution for the same.
Use the formula:
This is the inverse of Z value for the given 0.1 probability having default mean 0 and standard deviation 1 comes out to be approx -1.28. Now you can calculate the inverse of Z value for the specified probability values.
You can supply the probability value directly or using the cell reference. As you inspect from the above image that inverse of Z value for probability 0.1 and 0.9 has the same magnitude but different signs.
If you want to learn more about normal cumulative distribution, click here. This will enhance your understanding of the function with a random variable dataset.
Here are all the observational notes using the NORM.S.INV function in Excel
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