Normal Distribution Formula in Excel (Table of Contents)
- Introduction to Normal Distribution Formula in Excel
- How to Use Normal Distribution Formula in Excel?
Introduction to Normal Distribution Formula in Excel
Normdist function in Excel is under the statistical category, which is used to calculate the Normal Distribution of any data on the basis of Mean and Standard Deviation. Normal Distribution shows how the data points are distributed and the means and shows the standard deviation in both sides of the mean. To find the normal distribution of any number, we must first have mean and standard deviation mainly in the syntax.
Normal Distribution Summary
Normal distribution or Gaussian Distribution is a statistical distribution that is widely used in the analytical industry and have a general graphical representation as a bell-shaped curve which has exactly half of the observations at the right-hand side of Mean/Median/Mode and exactly half of them on the left-hand side of Mean/Median/Mode. This means normal distribution is a symmetric distribution around its mean.
The formula used to calculate the normal distribution probabilities is as given below.
Where,
Please note that the variable x takes values from -∞ to +∞
Syntax
Arguments in the Normal Distribution Formula in Excel
x – Required argument that specifies the value for which we want to find out the value for normal density or normal cumulative distribution.
mean – Required argument that specifies the mean of the normal distribution.
standard_dev – A required argument that is nothing but the standard deviation (square root of variance) of normal distribution.
cumulative – Is a logical value that specifies the type of normal distribution to be calculated. If set TRUE, it gives value for Cumulative Normal Distribution Formula. If set FALSE, it gives value for Normal Probability Density Formula.
In Excel, you can find out NORMDIST as well, which has the same functionality. However, if you will read the instructions properly, it is there just to use an excel file with version 2007 or earlier. After 2010 onwards versions of excel, NORMDIST is replaced by NORM.DIST. Maybe in the latest release of Microsoft Excel (Excel 2019), you may not see this version of the formula. We are going to use NORM.DIST in order to find pdf and CDF for normal distribution.
Let’s get the things caught up with some examples:
How to Use Normal Distribution Formula in Excel?
Normal Formula Distribution in Excel is very easy and simple. Let’s comprehend with some examples and how to use the Normal Distribution Formula in Excel.
Example #1 – Finding Cumulative Normal Distribution Probability
Suppose you are a working professional and it takes on an average of 40 minutes to reach the office. With the standard deviation of 10 minutes (10 minutes late or 10 minutes early) and the assumption that the time it takes you to reach the office is normally distributed with the mean mentioned above, what are the chances/probability that you reach to office in less than 48 minutes?
See the screenshot below for better visualization of this problem:
- In cell B1, there is a time we want to find the normal probabilities for.
- In cell B2, we have the average time taken to reach to office.
- In cell B3, you have the value for standard deviation in terms of time to reach to office.
- In cell B4, you will be calculating the normal probabilities.
Start typing the formula for normal distribution in cell B4.
The best thing about excel is that it gives you all the arguments associated with the function as soon as you type the keyword. As we can see here in cell B4.
Mention the first argument, which is the value you want to find the normal probability for, i.e. the value of x, which is already set in cell B1.
The second argument will be the mean time it takes to reach to office, which is already set under cell B2.
Mention the next argument, which is a standard deviation in terms of minutes to reach to office. It’s there in cell B3.
At last, mention a logical argument as TRUE as we want to find out the chances/probability that you reach the office within 48 minutes (or before 48 minutes).
We have set all the arguments that are mandatory to determine the cumulative probability that you reach the office within 48 minutes.
Press Enter key and see the output for this formula.
You can see that there are almost 79% chances that you will reach the office within 48 minutes. Consequently, there are 21% chances that you will be reaching the office in more than 48 minutes.
Example #2 – Finding out the Value for Normal Probability Density Function
Suppose, in the example above, you want to find out the chances/probability that you reach the office at exactly 48 minutes, then?
We will see step by step how to achieve this result as well.
Start typing the formula for normal distribution.
Input all the values for x, mean & standard_dev same as in the previous example. You can follow steps 2 to 4 from the previous example.
Now, instead of using TRUE as a value for the cumulative argument, use FALSE. It means that we don’t want normal cumulative probability; instead, we are interested in normal density probability.
Press Enter key and see the output for this formula.
You can see that almost 3% are the chances to reach office exactly at 48 minutes.
However, one point is to take note off this probability is also not the probability of exactly reaching the office in 48 minutes. The reason for so is, we have time as a continuous variable. Therefore, it’s logically impossible to reach exactly at 48 minutes. There will always be some portion of time which will be there after 48 minutes. Like 48.00000000005 minutes. That’s why in statistics, they say it’s impossible to find out the probability exactly at a point for a continuous random variable.
This is from this article. Let’s wrap up things with some points to remember.
Things to Remember About Normal Distribution Formula in Excel
- NORMDIST function is there to be compatible with older versions (2007 and older) of excel. After the version of 2010 and above, NORM.DIST function is used as a replacement for the same, and maybe from the next version of Excel (2019 and above), we might not see the NORMDIST function.
- DIST function is associated with the normal distribution of any mean. However, NORMDIST is associated with the normal distribution having mean zero and variance as unity.
- #NUM! error – this error occurs when the value for your standard deviation is less than zero.
- #VALUE! Error – this error occurs when there is any non-numeric argument passed under this function.
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