 of this number 64 is greater than or equal to the 79 which we're pulling that's represented here then I want you to take p of x if not double quotes which is just a blank space and that means that down to here you can see it 79 and above it's given me these numbers and you can see that that is given me then this orange spot at the at the cross now because we don't have a lot of data it's a little bit less than smooth if we had more data then it would be more smooth of a line but you can see it's basically right there and we have the side to the top being greater than the 79 so that is that one so then I can go and say okay well what if we're asking a question to have p of x less than or equal to this time 76 instead of 79 so we could once again make a dynamic type of label putting an equal sign before the p the quotes around all the text from p to the equal sign tying it together with an and to the number this case 76 and then tying that together with an and to the text under the quotes of unclosing bracket which allows you to change this number which will automatically change that number so then in order to calculate this it's just going to be simply the norm dot dist of the x 76 the mean and standard deviation 73.7 2.3 and then is it going to be cumulative yes this is going to be cumulative now if I was to graph that and look at it pictorially this is p of x less than or equal to 76 the formula then is going to be a logical test if the logic test is that this x is greater than or equal to 76 then is the comma then what do you want it to do pick up the p of x if not that's the second comma what do you want it to do leave it blank represented by quotes because text with nothing in the middle quotes of the text with nothing in the middle so you can see if I go down here it stops then at the 76 so if I was to graph this on top of what we had in our normal bell curve now you have the orange side being this side so now you the orange represents the area under the curve from here I think it's right there it's a little bit crooked because of the data being jagged because we don't have as much data but you get the idea of the orange being the area under the curve on that side you get the pictorial representation now of course the next thing we might do is well what if it's in the middle how are we going to graph that then well the next question we have we have p of x is less than 76 didn't I already do this so so we said oh we can also say that this is going to be one minus the the other bit if it was the inverse so I won't go into that here we're going to say now what if it's in between so now I want it to be in between 72 to 74 which might look something like this p of x is x I like to write it this way this might not be the x is greater than the equal to 72 and it's less than or equal to 74 if I do the formula for that we have to do two cumulative because if I look at it pictorially it would look something like this we're going to say that I want this bit in the middle but the cumulative function only works that it goes from left to right so what I have to do is say I'm going to take the cumulative up to the high point minus the cumulative up to the low point and that will leave me with the middle bit so it would be if I if I did the first bit it would be all orange up to here minus this first blue bit taking out that first blue so the formula looks like this it's going to be norm dot dist and then we've got the x on the upper x 74 the mean standard deviation are the same that they were before it has to be cumulative represented by a one minus norm dot dist with the lower mean the 72 in this case same uh the lower x 72 same mean same standard deviation and it also cumulative will will give us will give us that 32 15 the area under the curve now if I go up here and take a look at it we have our dynamic header up top this is another if then function that we could make this one which would be if and notice I have to have an and because there's two conditions now I'm combining an if and an and uh this is one way that we can do this right I can say well if and then and the logic text is that this number x over here x is greater than or equal to the 72 comma and then it's uh x is less than or equal to the 74 closing up the and function then what we want you to do is pick up the p of x we want you to pick up the p of x and if it's not true then we want the double quotes so it looks a little complicated if you practice it a few times not too bad so now it's picking up these ones right here is the only ones where we have our our information from 72 to uh 74 and so then I could plot that that's one way we can basically plot this you can imagine doing this a couple different ways but we can plot it that way and you get the amount in the middle now note this kind of indicates that every time we we work something like this we have to do multiple graphs to get a visual representation and remember that you don't necessarily have to do that because you could I mean you could use like a normal a normal graph like this and still get an idea of what is happening with a bar chart or you could use an area chart with just one of these separations and then change that point from the high point to the low point so you get a pictorial idea of what is happening when we're doing the the cumulative up to here and then the cumulative up to here so so there's various ways that you can make your graphs so that you can the point usually of the graph is to understand what you're doing in the calculations but there's multiple ways that you could make three different kind of graphs if you're doing an above below or in the middle but you might not need to have all that detail in order to get the benefits of a pictorial representation of the data