Hello everyone and welcome back. Now that we've talked about some characteristics of continuous data and how to summarize it in the last lecture section, and we also talked about various distributional shapes we might encounter including roughly symmetric and bell-shaped, left skewed and right skewed for example, we're going to talk now about a very specific theoretical distribution that many of you have probably heard of but we're going to look at some characteristics of it in detail. And that the distribution I'm talking about is called the normal distribution or sometimes the Gaussian distribution. So, we're first going to define this theoretical distribution and look at some properties of it, specifically, with regards to how far we need to go from the mean of the distribution in either direction to capture certain percentage of the data that follow that distribution. So, for example, we'll see that on normal distributions, if we start at the center and which is the mean and we go plus or minus two standard deviations in either direction, that interval will contain roughly 95 percent of the observations described by that distribution. Once we've established these properties, we'll look at applying these ideas to situations where we have a data set that's well approximated by a normal distribution. We'll talk about why no real life data can perfectly follow a normal distribution but there are situations where the data like we saw with the blood pressures for example, they're roughly symmetric and bell-shaped around their center and we can use characteristics of the normal distribution, the theoretical normal distribution to estimate characteristics of the sample distribution using only the mean and standard deviation. And then finally, we'll say this is all good but it only again works when we have data that are approximately normal and will show that if we miss apply some of these properties of the data that are not normal for example are heavily skewed and try and make statements about data ranges in our sample using just the mean and standard deviation and invoking the properties of the normal curve, we'll get nonsensical ridiculous results. And so, it'll just serve as a warning to not to blindly use the relationship between the mean and standard deviation for normal curves and apply it to non-normal data. The reason we're talking about this now is both that fits into the context of continuous data measures that we're working on but we're going to see later in the course that there are some theoretical distributions that we can't observe directly but we'll know are normal in shape and we can estimate their mean and standard deviation and we can put those three ideas together and make statements about this distribution we won't be able to directly observe. So, hopefully that what your appetite for learning more about this famous some might say infamous distribution and onward and upward with the normal curve.