 75 and then I typically say and and it's going to be I'm sorry x is going to be greater than or equal to 75 and less than or equal to 80. I tend to do it that way that might not be the best way right and that's the way I kind of think of it usually so so if you wanted to put so so there's now I could put make this into a dynamic thing again I can go into it and say this is going to be equal to quotes around this quotes after this bit and then that's 75 I'm going to say and to tie it to the 75 I'm going to replace the 75 with this 75 and then that and is actually something I want as a text field so this gets a little bit weird because now I have to say okay this is going to be tied to with an and and then that and I want as text so I have to put a quote around the and and then I'm going to go all the way from the and to the equal end quote and then I need an and this is not a text and but one that's going to tie it together the 80 I'm going to replace the 80 with this cell and then I have to tie that together with another and and then the text at the end is going to be quotes around this last bit and enter so that's so now I've got this dynamic thing where I can change the 75 to 60 if I wanted and it changes basically automatically down here put it back to 75 now if I wanted to do this then of course using the cumulative ability I can I can take this all the way up to the 80 as we did here which would be represented by the the orange and then subtract out everything up to the 75 so I'm going to say all right that means I have to do I could I could do it this way I could say this is going to be equal to I had I had let me let me hold on I got confused there for a second this equals norm dot dist so I'm going to pick the larger one which is going to be this 80 and then comma the mean up top is 74.2 to 92 again comma so I just hit comma so you can see it down here and now I'm on the standard deviation that's going to be the 10 09 again and then comma and then cumulative we do want it to be cumulative therefore one or true closing up the brackets and then I have to subtract out everything up to the lower point which will give us the middle stuff so norm dot dist again the x now is going to be the 75 comma the mean once again is 74 92 comma scrolling down just so you could see the argument so now we're on the standard deviation scrolling up 10 09 and then comma this also cumulative true or one close up the brackets and percentify home tab number group percentify adding some decimals and we get to the 1895 so notice that you have to be careful with the equal signs whether it be greater than or equal to now you might say well if I look at this I can say if I go to 75 here's the likelihood they get a 75 up to 80 what did I say 80 I can add those up I get to 18.7 remember that's not exactly the same here because it's the area under the curve so it's going to be like calculus and whatnot so it's a little bit different so this will just be that let's just put the same thing here we could do the same thing with Z's so I could take the lower Z and then the upper Z and do it with the Z scores the upper Z so now I'm just going to convert these two to Z scores so I'm going to say this is going to be equal to brackets 75 minus the mean which is 74 92 close up the brackets divided by the standard deviation which is 10.09 decimalizing home tab font group decimalize and so there's our Z and then I can do it here this is going to be equal to brackets we're going to pick up the 80 minus scrolling up we'll pick up the 74 closing up the brackets and then dividing by that's not a divide dividing by and we'll pick up the standard deviation and then enter decimalize home tab font group decimalize and so remember that the closer to zero that means it's you know in the next to the mean close to the mean right so now I can do my I can do my same kind of calculation with the Z scores so this is going to be once again this this will be equal to norm dot s dot dist and now we're going to take the Z I'm going to take the one related to the higher point which is the upper Z so this is going to be this one comma it needs to be cumulative therefore one close up the brackets minus norm dot dist not I'm sorry dot s dot dist tab the lower Z comma and then it needs to be cumulative therefore one or true and close it up percentify home tab number percentify brackets and we once again get to this one now this this is a little bit harder to represent with just our one graph over here so obviously I can see that upper limit of the 80 and then you can use the same one to visualize the lower by simply changing this to the lower is 75 right so I can change this down to 75 and I could kind of go back and forth in my graph and say okay it was between this line and then where it was before which was the 80 like when I went up to 80 over here so it would be nice if you can make a graph that shows both of those which we'll do in future examples but you can use this one graph to get some visualization of all of that together now let's play with our graph over here a little bit and see if we can make it a little bit more a little bit more fancy you might think it's impossible that's fancy as fancy can be already but no we'll add maybe a z score to it which will totally up the fanciness a lot so notice down here we've got our our amount our test score amounts and the middle point is over here we've got this line we might also want to be representing another x with our z scores so that we can also see this graph in relation to our z scores let's make this one a little bit smaller and then I'm going to say so so I'm going to add that to my graph I want to add another x down here so I can use either x and and refer to the z score or to the