 equation for the binomial distribution, which is binom.dist.range. Now with the binomial distribution, it's got this newer function than we had with the Poisson distribution we talked about before. So you can actually, there's a binom.dist and there's a binom.dist.range. The .range is designed to have more flexibility and it's also, could give you like the spill array kind of function. But the other function is still useful and it might, it might, because it might be more similar to what you're used to with regards to having a cumulative component, the last argument being cumulative versus not cumulative. So we'll look at both of them in a little bit more in Excel and in future presentations here, but we're using the latest and greatest one for this first example, which is binom.dist.range. So then we have the trials. So the trials are gonna be, gonna be the five here and then the probability is 10% per trial and then the numbers that we're gonna have is gonna be this range that what this, what this hashtag is, it's gonna spill out the, it's gonna spill it out here. So the likelihood then of having zero successes is gonna be 59.05. The likelihood of having one success out of the five is 32.81, two successes, 7.29 successes and so on and so forth. It's quite unlikely that we're gonna have four successes because each sales call that we have, we only have a 10% chance of success and getting four out of five would be very, you know, fairly unlikely in that case. Now we want to just get an idea of, of if we were to graph this now. So now we've got in one through five and we've got the percent likelihood going up to around 60 for zero, getting zero out of five, one out of five, two out of five and so on. So you can see you get a curve that looks something like this and now we just want to get an idea of feel for the curve as it changes when we change these variables of in and P. So if I was to change these variables to 10 versus five, notice now my X column in Excel because I used this cool rate sequence formula will actually populate automatically down to 10. And because I used a spill array, the fancy spill array formula for the binom.dist.range, this will spill automatically. So that's what's kind of nice about those formulas and you can practice that in our Excel presentation because it'll it'll populate this automatically. Now on the chart, it will actually populate automatically as well, but you might have to copy down the chart data range to make sure it picks up the full data range down to 10. From from the binom.dist standpoint, you can see it looks like this up top because it's stopping at zero, right? And now when you're moving it to the right, it's looking, it's going to approximate more of a bell shaped curve. So now that I've increased that. So if I do it again, I increased into 20 P still at 10%. Now we can see it's moving to the right and it's looking more bell shaped still being kind of cut off on that left side. And then if I increase it again and to be 50. Now it's out here kind of in the middle and you've got something that looks, you know, fairly bell shaped. That's that's going to be the general the general trend. When you're when we look at these curves, if I if I then plot this one back to five, but I increase P from I believe 10 what it was before to 20. Now we've got now we've got it being cut off again over here and it looks a little less kind of bell shaped if I increase it from from P of 40 probability of 40 to probability of 240% then I get it kind of moves to the right and you can see it's getting more of a bell shaped type of look here. And if we analyze this, of course, if P is 40% then the likelihood that we get zero calls zero successes out of five is now 7.78 the likelihood that we get one success is 25.92 the likelihood that we get two successes 34.56 if I'm thinking about the likelihood that I get from zero to two successes I would add these up right 34.56 25.92 plus 7.78 if I added that right 68.26 I'm not totally sure I added it right but that's the idea we'll talk more about that in future presentations right now we're just kind of focused on what the curve looks like. So if I then if I move this up to 50% now you've got something again looks somewhat more bell shaped. So as we increase N or P as we increase them then we tend to get something that starts to look more bell shaped. That's that's the general trend that you will see in future presentations will get more into detail with some actual kind of more scenario based problems.