In this short tutorial, we'll learn how to obtain the probabilities from the normal distribution In Excel. Normal distribution is one of the most important distributions in statistics. It is because a lot of naturally occurring phenomena falls under normal distribution. So you might be surprised to know that if we calculated the heights of everyone in the word and collected it and drew a distribution. It will end up looking like a normal distribution. Similarly, lots of other naturally occurring things follow a normal distribution. So it's an important distribution to know about. Now in this Excel sheet, I have a few values and to just to save time, we're just going to see what these mean. So I have, in the first column, I have titled it as values. And these are the values that we're going to get probabilities for. The next two columns show two different kinds of probabilities. Now these probabilities come from the normal distribution, but their nature is slightly different. The PDF refers to the probability that depicts -- that depicts the approximate probability of a value occurring under the normal distribution. Now technically speaking, the probability of exactly something happening or getting a value of exactly minus 3 is 0. But if we take a small interval around it, a very, very infinitely small interval around it, it'll have this small probability, 6.69 to the power of minus 5 So how do we get this? Well, it, we get this from a function called norm.dist for normal distribution, which takes four parameter values. The first parameter value it takes is I have depicted as A2, and that's just this number. Minus three. The second two values it takes is the mean and standard deviation. So F1 is this particular number, 5, and then F2 is two. So the mean of the distribution that we want to draw the values from is five and standard deviation is two. So these are the two parameter values that we have to specify. And the final parameter value is either 0 or one. 0 stands for whether you want the cumulative probability or not. Now again, as I mentioned, the pdf probability is the probability that a particular value will occur. Whereas CDF probability is that a number equal to or less than that value will occur. So this probabilty here, 3.16 to the power minus 5 depicts the probability that a number minus three or some number smaller than that will occur. So that's called cumulative distribution function or CDF. If you want the PDF value, you specify 0. But if you want to get the, if you want to get the CDF value, then you just specify one. So that's the difference. Now, to get a little more intuition into these values, Let's graph these. So I'm going to choose column A and column B. And then I'm going to insert an x y graph. And so here we see the nice bell curve that depicts the normal distribution. Again, what it's saying is, so for example, if I drew a line around the number five, which is the mean of this distribution, we can see the probability it depicts is around 0.2. So the probability that a number around five will occur is approximately 0.2. Now let's compare this to a CDF graph. So let's draw another graph. I'm going to choose column A and column C this time. And again, insert a new graph. And now you can see the CDF probability. Now these are, remember the cumulative distribution function looks like what we call a sigmoid graph or an S curve. Looks like an S. So here. Now if we look at the probability associated with the number 5 or the mean of the distribution, we can see that it's going to be 0.5. So, so what it is telling us is that the probability that a number five or something below that will occur, If we draw a number from a normal distribution with a mean of five and standard deviation of two, that probability is 0.5. Now that makes sense because if we see our PDF, which shows us the distribution shape, we see that it's asymmetric distribution. So the probabilities are distributed the same way as they are on the left-hand side of five, as well as on the right-hand side of five. So in either direction of five, we have the same distribution. Therefore, the probability is exactly the same at five, whether you have less than or greater than five. Now this is a very useful, the CDF is a very useful function. This is what we will normally use in our analysis in doing simulation. So you should familiarize yourself with norm.dist or normal distribution function in Excel.
