 off and on back it again, Alt equals, there's the sum function automatically populated, comes out to one or if I number group percentify it 100%. Okay, doke, so there we have that. Let's go ahead and make this into a graph and possibly graph it to see how closely it matches up to our data on the right. So let's do that. I'm gonna select, let's just select this data. And I'll select this entire thing. Not the total though, not the tote. And then scroll back up, I'm gonna go to the insert tab. Let's go to the charts group and insert a chart. And so there we have it, nice smooth curve. So then I can go to my data up top and I wanna make sure that this data on the right is picking up my numbers. I don't want it to just make up, just make up your own thing. No Excel, these are the numbers you use. You use my numbers, that's how you do it. Don't just make up stuff. And then we're gonna say, okay. And then let's add also comparing that to the data that we actually counted. So I'm gonna add another one here and I'm gonna say, what's that data? It's coming from, and I wanna pick up the percent ones. And then the data, I'm gonna delete this and hit this little thingy and control shift down. And then control or shift up. So I don't pick up the 100. And so there we have it, okay. And okay, I think that should do it. So let's go back on over and check it out. So there's our data. So you can see it's not a perfect lineup but you can see it's fairly well approximated, right? And let's do it again with a line graph. You might want a plus and a legend down here. We should probably label our graphs better but I'm gonna keep it at that. We could also scroll down and I could make this, well, let's keep it down to 100. Let's do another one. I'm gonna do this again with a line graph this time. So let's select this whole thing. Ultra base, another time. And let's just bring it down to like something a little bit less. Let's bring it down, I don't know, to 70, let's say, 70. And then I'm gonna go into insert charts. Let's do this one this time, lines this time. Boom, let's do that one. So I'll bring it down. Let's format this thing. We're in the chart design data. So I'm gonna say the other data here. I don't want you making up your own numbers, XO. Dude, these are the numbers you want down to 70. That's what you do. That's what you do, you hear me? All right, and then I'm gonna add another data set over here representing our other data. Over here, total percent. And let's pick up this. It's gonna be equal to down to 70 again. I'm just gonna go down to 70. And boom, okay, I think that's good. And okay, let's check it out. Check it out, man. So there we have it. So you can see it's not a perfect, but it lines up pretty well. And so now we're thinking, so we had this one that kind of outlined in our data set was kind of interesting, but it lines up pretty well. So you would think that we'd have some predictive power using the Poisson distribution, which would be easier to make predictions into the future than trying to extrapolate out some just random set of conditions. Otherwise, it's gonna be a lot more complicated for us to try to figure out how to extrapolate out just a random set of items, as opposed to an actual curve that we can plot into a formula, right? So, and then, so that is going to be that. Now, we could also ask questions such as, what if, let's make Z a little bit smaller. What if we wanted to see how many potholes are from pot? So we wanted to say like zero to five. So let's say equal to and including five potholes. So now I'm including five, that's always gonna be one of the sticking points. So in this particular one, you could sum that up equals the sum of our data here and say, okay, boom, boom, boom, boom, boom. And then make that a percent, home tab numbers percentify. And so you're down to 0.007, right? So that you get between zero and five potholes from in a hundred mile span. I could also do that with the cumulative. So if I didn't plot this data, I could say equals poisson.dist and then I could take my X value is going to be, I'm gonna say five, it's going up to and including. If it was not including five, I would have to go up to four, right? Because if it was up to but not including, so you've gotta be careful if you're working book problems with this. And then the mean comma the mean, and notice I picked up a mean here of 20. Notice the mean that we actually came out to with, well, let's keep this for now. And then I'm gonna say comma, and then this time I want it to be cumulative so that it picks up to that point, not probability of mass function. Therefore, we're gonna put a one here and close it up and add some percents. And there we have it. Now notice when I generated this data, we generated it based on this 20, which is a little different than the actual data we came with our test. In other words, if I change this, I could change this number to this 20.14 because just, which is pretty close to the same because what happened here is we used the 20 to generate the random numbers. And then when I created the random numbers, the mean of the random numbers is actually 20.14. So if we imagined doing the actual experiment, it would be 20.14 would be our mean that we would probably then want to use in our Poisson distribution when trying to extrapolate forward. So in any case, there is that. And then you could have questions like, I mean, it's likely that you're gonna have a question like, well, what if it's going to be, and you're probably gonna say questions likely are gonna be what's the likelihood that you're gonna have up to 12 potholes. But you might have questions like, well, what if we had between, I'm gonna say, equal to and including seven to, you know, 14 potholes. Now, again, when I say seven to four,