[SOUND] In lesson five I showed you this side where I found the probability of x between 1005 and 995 to be 0.3829 when we have a distribution which has a mean of 1000 and a standard deviation of 10. I ask you to watch the video in Excel to know exactly how I came up with this number. So this is what I'm going to show you today. Here we have, mean of 1000, standard deviation of 10, and we're asking for a probability of x being between 995 and between 1005. One of the thing that is very helpful at the beginning when you're trying to learn how to do the normal distribution is to draw it. So I'm going to show you what this looks like in picture, so you can visualize it and that way you would understand what the software is doing for you much better. So if I can visualize this curve, and forgive me if this is not perfect because I'm not very good in drawing but it would be a symmetrical curve, normal curve that looks like this right. And it would have a center, a mean, that is 1000 and we are talking about what is the probability of it being 995 And 1005. And if I can draw this in terms of probability, and see the shaded area, this is what they're talking about. So this is 1005, and this is 995. The way Excel works is that if I give it a value of x to be 1005, it's going to give me everything to the left of this. Same thing will happen if I give it 995, it will give me everything to the left of this. So as you can see, if I take this larger value, and subtract from it the smaller value, I should be able to get the value. So let's just do that and see what is the function that I will use. So first I'm going to look at the probability of x being less than or equal 1005 that's the larger area. And the function I'm going to first show you is the simple function of NORM.DIST. You can see that there are four function that comes up that starts with the word norm. These are all for normal distribution. Here, I'm going to only focus on NORM.DIST. So I'm tap on that, and you would see that the first argument they ask for is x, x here is 1,005 and that's your variable of interest. Mean here is 1000, standard deviation is 10, and the last argument asks, if you're looking for cumulative distribution function. And the answer to that is yes. True, so you can either enter true or can put value on one. One gets translated to true, zero gets translated to false. You will actually not have any occasions in this class where you have to calculate the probability mass function as it's called by Excel. So you always have the last argument for use at add one. So put one there, close the parenthesis and press Return. And what you get is 0.6914. So what is that? That is basically this shaded area in yellow, 69% and it makes sense, right, because everything to the left of the mean is 50%. We're a little bit to the right of the mean so it has to be more probability. So we have found 0.69 would be the yellow shaded area. So now we're going to find this area. So, that is probability of x being less than or equal to 995. So I will repeat the same thing. What is the probability of x? Less than, and you can see that Excel tries to be helpful. You don't need to use it, but it is there. So it's going to be NORM.DIST, and again, I will pick this. And the only thing that changes now is that NORM ix is 995, mean is 1,000, standard deviation is 10, and the last argument is one. So there we go. The green area Is 0.30 so the shaded area in yellow right now. What I'm looking for is going to be the difference of the larger area minus the smaller area. 0.38292 which is exactly what I've showed you in our power point presentation. In the next video, I'm going to show you how to do it if you were to follow this steps verbatim. Now, the only reason I'm showing you is because I want you to know how the functions work. In real life, obviously, you pick whatever that's best for you. I like to use what I showed you just now because it's the fastest way of coming up with it.