 So we'll take control shift down and enter. And so that's 75. So we're gonna say home tab number group and adding decimals here. Now the fact that these two are similar in our actual data is one indication that it might actually follow a bell curve system. Notice that not all data follows a bell curve, but a lot of data you would kind of assume would. If you're talking about errors, for example, that's the classic example of when bell curves came about is when they were trying to make predictions. People never got it exactly right, but they had errors like where the stars are gonna show up in the sky or whatever like that. You know, you can have errors that hopefully will average out to the actual answer. And so you would think same with test scores, you would think height, a lot of things in nature you would think, but a lot of stuff doesn't conform to the bell curve. So it's just like the other curves we talked about in the past, we wanna say does it conform to a bell curve type of system? And if it is something that you would think would conform to a bell curve like grades or something and it doesn't, then again, that's a question to say, well, what is going on here? Because it was something, because you would think it would and then you dig into why maybe it's not. Okay, so let's make column H smaller and then I'm gonna make a histogram. This is another indication of if it would be a bell curve. I'll select the name up top, control shift down, all the data. Now I'm gonna hold control backspace to get back up to the top without unselecting the data and then insert tab. We're gonna go into the chart. So I'm gonna just make a standard good old histogram. There it is, histogram of the data. So boom. So now this of course giving us our buckets down below I let Excel just choose the buckets. So it chose these buckets and maybe I can format this data. If I format this data and I say, let's go to formatting and say that we want to have it to be, let's say currency negative numbers bracketed two decimals. And so now we've got some brackets, some data that's not so chaotic with so many decimals down here. So these you'll recall are the ranges that it's gonna be putting in and then it's counting the number of occurrences within the thousand that fall into those ranges and this middle point of course where the most occurrences happen is around that 75. So if we put the focal point here it'd be around the middle. Notice this doesn't look exactly like a bell because we only have a thousand data points but it approximates a bell and if I drew a smooth bell curve on it the question is would that bell curve give us predictive power into the future? And the assumption here would be yes because it looks somewhat bell shaped, right? So now that's what we'll do now. I'm gonna pull this on over to the right and say, okay, I think the bell curve is applicable and this situation would be our determination. And so now we're gonna actually plot the smooth bell curve which will be more exact, just a smooth curve. And notice that the calculation of the bell curve, the formula is a fairly complex formula but the point of the bell curve usually isn't to try to understand the formula exactly, although that's a good exercise. It's to say, well, how can I apply? Whoever made the formula gave us a great gift, right? Because now we're able to apply that to these situations using tools such as Excel to approximate our data. So I'm gonna say this is gonna be X. I'm gonna say this will be P of X. And so let's start with those two. We'll plot our data out. I'm gonna go to the home tab, font group. Let's make it black and white. I'm gonna center it, alignment center. Let's make this one a bit smaller. All right, so just to get an idea of what we can do now, we're gonna say what should our Xs be, right? We could have a lower limit and an upper limit basically on the Xs. Now we could just have Xs go from zero on up to 100 or we might try to say, hey, look, I'm just gonna go four standard deviations out and that's usually enough to capture all of the data. So the way the bell curve basically is going to work here, of course, is that most of the data is gonna be in one standard deviation and then within two standard deviations, a large part of the data is gonna be there and if you get over three standard deviations, very small amount of the data would be outside of that range and then so four standard deviations again would basically encompass almost everything, right? So if I'm trying to say what should my Xs be, what should be the bottom part and the top part so I can plot my graph, if I choose four standard deviations, I'm gonna be picking up most of the data. So let me show you what I mean here. We're gonna say if I took a let's call this lower X and then the upper X for our chart. So these are the chart X areas, the lower and upper. So I can say, all right, this lower amount is gonna be equal to the mean, which is the middle point. That's gonna be the top, the tallest part of the bell curve and then I'm gonna say minus because it's the lower point minus this 10.09 which measures the spread and I wanna go four standard deviations lower. So I'm gonna say times four. So let's pull this down a bit. I'm gonna pull this down and I'm gonna say standard deviations and let's say four like that. So I'll do it this way. So this minus that and then I'll say times four and I can point to it there and then maybe I should add some decimals. Okay, and then the upper, the upper limit is gonna be equal to the mean, the middle point, plus four standard deviations. One standard deviation is 10.09, part of the spread, times four, we want four of them and that'll give us 115. So we're gonna say then the range is gonna be from 34 up to 115. Now, obviously again, it might cap at 100. So the 115, when you think about a bell curve in general, remember that the tails of the bell curve can go out forever in a theoretical bell curve. Obviously from a practical real-world example, there might be an upper or lower limit, in our case, the lower limit generally being zero and the upper limit 100. But if I was to capture four standard deviations, this is the range that we can pick. So if I was to say I'm gonna try to plot this thing, then instead of starting at zero, I could possibly start at 34 about and that would pick up pretty much all of the data. So I could say, let's go from, and now I could do this with like, well, let's do it just this way. I'm gonna say 34 and then 35. I'm gonna select those two and I'm just gonna bring it on down till I get to 116, right? So that should capture all of the data. And you can see the number format, I can go till I get down to 116 right there. That's when it happens. And that should capture all of the data, the primary part of the data. So then I'm gonna say, all right. And then now let's actually just plot it. So if I go over here, this is gonna be our norm.dist function for each of these X values. So I'm gonna say this equals norm.dist. So norm.dist, this is gonna be our major function. Here's the arguments that we need to input in order to get the result for it. So we're gonna say norm.dist has an X value of 34. Now I'm not gonna do an array right now. I'm gonna do it basically without an array formatting. And then comma, the mean is gonna be this mean, 74. I'm not gonna use the mean that we used when we first started, it's close, but not exactly the same as the mean of our actual data. I'll use the mean of the actual data. And then I'm gonna select F4, making it absolute dollar sign before the G and the two comma standard deviation. The spread is gonna be that 10.09 F4 so that when I copy it down, those two cells will not move down comma. And then this is whether we want it to be cumulative or not, which is similar to the arguments if you saw the, if you saw our presentations on the Poisson distribution and those other distributions, they had some of them have this similar kind of argument, but it might be a little bit different when you're talking about the normal distribution because you're talking about the area under the curve when you're talking about the cumulative, meaning there's kind of calculus involved because you're talking, or possibly because you're talking about the area under the curve, right, so integral, so, but so, but conceptually similar kind of concept to it. But we wanna have it as of a certain point. So I'm gonna say zero to make it false or you can type in false or you can put in zero, zero is easier to type. So I'm gonna close it up and spell. And then I'll, let's make that a percent, home tab, number group, I'm gonna percentify this, add some decimals, and then I'll double click on the fill handle and that'll copy it down. So I can copy it down and so we can, we can, for example, look at the, and by the way, if I select this entire thing, control shift down, oh, what did you do, Excel? What?