um in particular in Excel the command uh Norm s dist uh takes a zcore and tells you the area to the left which is the same as the probability okay and we talked about drawing the picture which is going to be very uh useful and crucial going forward all right so we talked about finding the area to the left in other words for z is less than we talked about finding the area to the right for example Z is greater than what didn't we talk about that's where we pick up today how do you find between area so we don't know how to do this question in full yet but we do know how to start what's the first thing you should do draw the picture absolutely okay so let's draw the picture so here we have a picture what should we label on it and where does zero go okay and zero goes in the middle for what this is a zcore so make sure you label that this is a zcore all right uh what else should we label what else should we mark on the picture sorry absolutely so here is 1.26 and here is 2.18 and what else should I mark on the picture well what are we trying to find oh yes you skipped right ahead so we're trying to find a probability and how do we represent probability probability is the same as area so which area are we trying to find right so we should Mark that off there we go so that's the area that we're trying to find the question is how do we find that area Excel can only tell us area to the left so how can we use that in order to find this between area absolutely subtract what uh no so your first idea was right uh or the the the start of your idea was right though we do have to subtract what do we subtract have find the are um will the area to the right of 2.1 six would be this area so can we do something with those two things to get the area in between I guess we can but there's an easier way instead of the area to the right of 1.26 get the area to the left and once you have each of these areas how can we find the between area subtract take the purple area and so what is on the picture what is the purple area the purple area is this and then we can find the orange area which is this and if you take the purple area and take away the orange area what's left the between area that we're trying to find okay so now we have to find each of those areas so how do we find the area uh to the left of 2.18 so this is what we talked about last time uh the Excel command Norm SD gives us the area or probability to the right to the left of a zcore so equals Norm s dist of 2.18 and that is we only need four places right there 9854 now let's find the area to the left of 2.16 Norm s dist of 1.26 and that one is 8962 so in order to find that in between area what do we have to do subtract what what numbers yep and you do that and you get 0892 and that is your middle area or your between area now it's blue again okay so I want to get back um Elizabeth to something that you said uh your first instinct was was to subtract the zc scores um which is a reasonable guess but it's wrong and it's a very common error so I want to talk about it right now so first of all which which values did we subtract we subtracted 8 9854 and 8962 what kind of values are those these are probability values exactly Chast okay these are probability values now what happens if we try to subtract zc scores which is the wrong thing to do if you subtract Z scores well 2.18 minus 1.26 that gives you .92 so that would give you a zcore of 0.92 having the zcore of 0.92 does that help you do anything in this problem no zore .92 has nothing to do with this problem at all so subtracting zores is the wrong thing to do is that Mak sense so again subtract area values to find that between area all right all right so use your handy computer and do this problem okay so we we're going to work through it together and you'll have it uh next time everyone will uh will have a computer and you'll be able to work through some of these uh on your own okay so what's the first thing we do sorry nope draw the picture yeah okay um oh okay that's not terribly symmetric all right so now that we've drawn the picture what is the uh how do we label it zero and that's the value for what Z so remember to label these uh for Z okay and what else do we label okay and now what shap where there you go okay so that's the area we want so what do we have to do or find yes for what okay right so first we'll find the area to the left left of 1.22 and that's Norm s disc of 1.22 so that one's 8888 all right next we'll find the area to left at - 2.67 and we're going to type Norm s disc now by the way what do Norm let's remember what does Norm s disc stand for normal standard disc distribtion distribution right okay so this is -2.6 so this one is 00 38 and now subtract uh if you do it correctly yes okay and that's it yeah if you want to write it down I mean I didn't copy the question you could just write probability - 2.67 oops less than Z less than 1.22 equals this thing if you don't write what down no I wrote down cuz she asked however uh I will say something important about this notice how many different decimal numbers there are flying around in this entire problem there's the 038 here there's Point there's lot there's going to be lots of members when you do these calculations Circle your answer so I know which one is your answer if it's not clear to me which one is your answer I can't help you okay