 14 you've got to be kind of careful and say well what do you mean by 7 do you mean it's including 7 or do you mean you're going between 7 and 14 most of time when people talk and just common language they're saying what's the likelihood that you will and be including 7 through 14 but book problems you got to be quite careful if they're saying between 7 and 14 but not equaling 7 and 14 then you got to make sure you're picking up the space between now how would you do that well if I plotted it out I can just take the sum here of from 7 to 14 right 7 to 14 and then percentify that add some decimals if I'm using my cumulative then I've got to take the cumulative up to the top point which in this case is going to be 14 if I'm including the 14 then I'll go up to 14 if it's not including the 14 that I have to go up to 13 that's we have to be careful and then I subtract out everything that I don't want to include which is up to 7 so so I want to subtract everything out that I'm not including so that means I'm going to go up to 6 because 7's equal so it'll look like this we'd say this equals this equals Poisson I forgot what we're doing in a second here Poisson dot dist X is going to be the higher one 14 because I'm including the 14 comma the mean is that 20 point 1 4 and then comma it needs to be cumulative or 1 that'll sum everything up you can imagine basically up to the 14 closing it up minus Poisson dot dist and then I want to subtract everything up to but not including the 7 because I got subtract because I don't want to take out the 7 bit so I've got to go one down so I'm going to take everything out down to 6 comma the mean is 20 point 1 4 comma and it's going to be cumulative again or 1 close it up and enter and so there we have it so I'm going to say boom so notice when you're working like book problems more likely you're going to have these kind of calculations in practice it's quite nice of course to actually plot out you know the whole thing here and then and then and then that gives you a more pictorial view of what exactly is going on which in practice I think that would be you know the way to go if you're trying to explain to somebody what is actually happening here it's probably easier to do if you plot the whole thing out and say okay this is what we're doing instead of just entering the Poisson distribution like this and just saying well here's the prediction based on Poisson right because that's not going to be too intuitively understandable to a lot of people that don't know what you're talking about any case let's make this whole thing bracketed let's put some brackets around this thing and format it let's do some formatting here oh by the way so we have this data the other the other thing we might do is see how close this data lines up to to what we got so let's make one more right click I'm going to insert one oh not delete right click insert and let's just make this is the diff for ends so let's just see this is going to be equal to what we got minus when we when we counted the potholes minus hold on did I pick up the right one getting a little tired a little distracted here focus what we got minus this and then I'm going to copy that down and so there's our our differences that's another way you can kind of look at it and say okay how close is the poisson versus the data that we calculated on our testing all right let's go ahead and format some of this so we're going to say there's that let's I'm going to select this whole thing control shift down make it blue and bordered home tab border it drop down on the bucket I'm going to make it blue if you don't have that blue it's in the more colors standard blue you don't have to make it blue but that's what I do and then control shift down and then border blue the blue is just a happier color than the green for me green reminds me of the days of the spreadsheets where I had terrible handwriting and and I couldn't even read my own writing but I tried so hard with my ten key before the time in the in the dark ages before the before the Excel times there was Excel but people still insisted on on forcing me to do like a ten key and the spreadsheet and it was it was cruel I think it that was the point honestly it was supposed to be cruel and unusual punishment and it achieved its objective okay so let's do a spell check on it maybe a spell check that'd be nice you spellchecky potholes potholes all right there we have it