 is greater than or equal to 133. So if we're looking at our graph over here, we're saying, if I look at this graph, this, by the way, is graphing this p of x and the actual data as a percent so that we can put them kind of on top of each other and we can see that the actual data lines up pretty closely to the curve in this case, which is an indication that the curve would be half good predictive power. So now we're looking, we're trying to find another way to graph our curve in an area graph this time which might help us to use one graph to that could vary possibly between different scenarios. So we have a question of something being above would be the blue part. So I can kind of look at this line and if it was below, I can look at this line and below and if it was between, I can look at basically the between area. So here's our questions here. This one, this question is a question for us to have it greater than or equal to 133. So if 133 is here, we're looking at the blue kind of above that point. Okay, so if we visualize that, we're gonna say, well then it's gonna be above, so I have to use one minus. Why? Because remember that I can only go from left to right and use the cumulative. So I can't go from right to left. So if I'm going, if I'm looking at this blue area on this side, I have to say I'm gonna take the whole thing minus everything up to this point, which will leave me this bit. The whole thing being 100%, 100% is what the area is under the curve, 100 represented by one minus the norm.dist of the x, which is the 133 comma the mean and the standard deviation 127, 11.66, comma cumulative, yes, it needs to be cumulative. Okay, and then I could say, well, what if I do this in terms of z scores instead of x? So let's convert that x to a z score. That would be 133 minus the middle point, which is the mean of 127.08 divided by 11.66. So the z score then is about 0.51. So if I knew the z score, which is a little bit over, you know, it's over the middle point, which would be zero higher than the middle point of that, then I can use a similar formula, which would be one minus norm.s.dist. All I need is the z because the x mean and standard deviation have been kind of combined together when we calculated the z and it once again is cumulative. We get to the same result of the 30.58. Okay, so then I can do this kind of question. x is less than 109. So if I go over here and say, okay, well, if x is less than, I can look at these. So notice if, well, let me graph this first. Let's graph this other one. x is greater than 133 or P of z is greater than 0.51. Then this is gonna be if logic test and we're picking up this x and saying if it's greater than or equal to and we're picking up the 133, then comma, what do we want you to do? We want you to give us the P of x, but if it's not, then we want you to just put blank there, which is double quotes, text field with nothing in the middle. We could have done the same thing with the z score of 0.15, right, the z score or the x. And then there's nothing in it until we get down to, way down to here, which is the 133. And if I graph this on top of what I had on this side, then it's gonna give me that separation. So now let's, but let's go to this one. We want x to be less than or equal to the 109. So less than, so if we had 109 right here, we're looking at the blue side in this case, we want it to be less than. Now, because the cumulative is up to and including that point, we could just say up to and including that point. Remember that you might also say, if it's 109, you might say, well, look, 109 is right here. Why don't I just sum up from 109 down to here? Cause I can do that easily in Excel, but that'll be an approximation, not exact cause we're looking at the area under the curve. So to be exact, you'd want the formula. So we could do the formula over here and it'd be looking like this. It would be equal to the norm.dist. The x is the 109, the mean standard deviation, 127.08 and 11.66. Do we want it cumulative? We do therefore a one and we get that 6.05. We can also take the z score. So if we represent x as a z now, the 109, I'm gonna convert to a z by subtracting it minus the middle point of 127.08 pounds divided by the standard D 11.66. And we get to that negative 1.55, then I can use my norm.s.dist to get to the same 6.05 using just the z and it being cumulative, the z now taking into account has combined together in x essence, the x, the mean and the standard D. All right, so now let's take the middle question. So now we're gonna say, well, what if p of x, x is less than the 133 and it's greater than the 109. So if I was to, if I was to look at that over here and say, okay, well now, now we have it less than less than, I think if it was less than here and greater than here, 109, 133, it's the orange area. So how would we do that? Well, I can only add it up up to a certain point with the cumulative. So I would have to add the higher end up to here and then subtract out the cumulative of the blue area in order to back into the orange area. So I'd have the whole thing up to here, all of the orange and then minus this blue bit. So notice that if I, let's first think about how I graph this one. This is x is less than or equal to 109. So that's going to be our if calculation up top. So if we're going to say logic test, this 80 is greater than or equal to the 109, then what do you want to do? Pick up the p of x. If it's not comma, what do you do? Put a blank thing. So now you've got data from here down to here and then it's all blank. So if I graph this, so you can imagine I graph this on top. So I have another layer on top of my graph here. And then this last one over here, we're going to say that, and also I have a dynamic.