 times because you have certain formatting within the tables and I feel like it's less likely that you're going to kind of mess up your data when it's in the table such as you know sorting the data on one column without sorting the data on the other column. When I'm in the table I can also go to the table tools up top. We can add a total column and if I sum this up you can see that this sums up to 100% that'll give us kind of a check figure that what we're doing is correct. However if I go back up top here you'll recall one of the benefits from the prior presentation you may recall is that now I can adjust this number a little bit more easily. So if I adjust this number and say I want to make it 15, notice now because we used a spill sequence it'll now increase to 15 automatically and so I can bring it back down to 12 so you have a bit more flexibility with these ones. Just note with this binome.dist.range the arguments are a little bit different and they're a little bit more flexible. We don't need the cumulative argument as much because it allows us to enter multiple arguments which allows us to kind of pick the middle of the range a little bit more directly as opposed to what we did with the Poisson distribution if you recall if you saw all the prior presentations where we had to do the cumulative up to a certain point and then subtract out the cumulative up to a different point in order to get that middle range. So it's a little bit, it's got a little bit more flexibility. Okay, let's go ahead and graph this thing I'm going to make column F a little bit skinnier and then let's select our data and so I'm going to go up top and go to the insert and then we'll go to the charts and we'll enter the bar chart and add our bar chart so I'm going to pull that to the right and then do our standard process I'm going to click on it go to the data up top and I would like to go to the edit of this side to make sure it's picking up our X numbers which are going to be from 0 to 12 so I'm going to say okay and okay and so there we have it I'll just delete this top it and so so there we have it and you can see of course that it kind of in the middle point is that six as we would expect we can also plot it with the line chart to so I can select these insert we can then go to the charts and have a line chart something like this one and have it look like this format I'll do the same thing here I'm going to click on the data and select this one and say I want to make sure that you pick up my numbers here 0 to 12 and okay okay so we can format it like that and it looks kind of like what you would expect at the middle point being six so let's do a little bit of an analysis similar to what we did in the prior presentation if we think about our data over here if we have a fair coin 50 50 on the coin flips remember if I flipped it zero times if I had zero flips then if I define a success as heads then I'm not going to get any heads of course so a hundred percent likelihood that that it's going to be you know at zero right zero and then I'm going to say if I have one well then if I have zero successes the likelihood is 50 percent the likelihood if under two flips that I get one success defined as a heads is 50 percent if I say two then now we're going to say okay if I do it if I do the flip two times the likelihood that I get no successes defined as heads 25 likelihood that I get one success defined as heads 50 likelihood that I get two successes both heads is 25 percent and if I go to three then you can see it's likelihood that I get zero successes out of three flips 12.50 one success out of the three flips 37.5 two successes out of the three flips 37.5 and three successes they're all successful heads 12.5 and then four and so on and so forth so you can see how this is being built and we looked at the changing of the curve on the right hand side in a prior presentation as well so let's put let's put it back up to 12 so now we're saying 12 times we flipped it and by the way one other thing to look at if the coin was not fair then if it was 60 like let's say you know it's going to land 55 percent of the time heads so it's it's slightly tweaked the casino tweaked the coin or whatever right so now if I go if I flip it one time now it's got a if we have zero successes zero heads if it's in our favor that it's 55 percent heads then it's going to be 45 percent no heads 55 that it will be heads two per two times now we've got only 20.25 no heads 49.5 that we get one head out of the two 30.25 two heads and so on and so forth so we'll consider it a fair coin we're going to flip it 12 times it's going to be back to the norm here back to the where we started so now let's mirror the experiment so instead of us using simply a random number generation as we saw in prior examples whereas if I was going to simulate each coin flip I can say equals random you know between one and two having one represent heads two represent tails but instead we're going to get a little bit more sophisticated here and go to the data tab and we're going to say that I want to have the data analysis tool help me generate the outcomes of 12 12 flips according to the rules that we have here so I'm going to say these are going to be the outcomes that will generate let's make this home tab font black white center it I'm going to put them here and then in the data tab if you don't have this analysis section you go to the file tab and then options and then add ins and then excel add ins and go and you want to take that analysis tool pack and if you have that tool pack then you've got our tools in the data tab so let's open that up and I want to go to some random generation numbers and we're going to say okay and I'm going to say one here that's basically the number of columns number of random numbers let's go to a thousand like have we've been doing customarily this time we did this with a poisson distribution this time we want to get the generated numbers in accordance with a binomial distribution p we remember is point is a point five fifty percent and the number of trials n is going to be twelve so we're going to have twelve flips with a p of fifty percent for each of the flips and then I'm going to put down here the output range where do we want to put it I want to put those thousand numbers right there so that's going to go to p2 and I'll say okay and now it's simulating these these tests right so now we flipped these are representing for example one test of 12 flips where I've got five successes which we define as heads right so five heads out of 12 seven heads out of 12 seven heads out of 12 four out of 12 four to 12 four to 12 nine out of 12 and so on and so forth so let's put those results into a bucket if we could so I'm going to make this a little smaller and I'm going to say this these are going to be our bends and this is going to be the frequency now when we have the bends are going to be anywhere from zero up to