Remember this diagram? In the video, population versus sample, we discussed taking a sample from the population. From the sample, we computed estimates like the mean, and the standard deviation, to describe the observations in the sample. In this video, we are going to talk about this curve, the probability distribution. In statistics, a histogram represents a sample and the curve represents an entire population. In this video you will learn to distinguish between different types of probability distributions. I will also show you that in a Lean Six Sigma project, you mostly encounter a normal, lognormal and Weibull distributions. In the video on probability plot, I will teach you how to determine which of these distributions fits your data. There are hundreds of different probability distributions available. And you can find many of them in Minitab. However, in all the projects that I have seen, I have mostly encountered just a few, which makes life a lot easier. You will come across the normal distribution, the Weibull distribution, and the lognormal distribution. So I will focus just on these three. And let's start with the normal distribution. It is symmetrical. And it looks a little bit like a bell shape and that is why it's also called the bell- shaped distribution. Let's illustrate this with an example. I tested the caffeine percentage in coffee and found a histogram that looks like this. I also found a mean of 0.078. And a standard deviation of 0.020. You can see that the data looks a little bit like a bell. It's symmetrical around the mean. The blue bars in the histogram show the distribution of the 50 values in your measured sample. The red curve is the population distribution that Minitab fitted to the data for us. When the number of measured values is just 50, you need some imagination to recognize the normal distribution. However, as the number of measured values becomes larger, the distribution converges more and more to these bell shapes. The more N increases, the more it starts to look like a bell shape. You can use a normal distribution to make some simple calculations. This is discussed in the video on properties of the normal distribution. Let's look at another example. I have collected data on throughput times of handled claims at the bank. And this is a histogram of our throughput times. I can fit the normal distribution curve. Does it fit well? The answer is of course no. The histogram and a normal distribution curve have different shapes. And therefore we say that a normal distribution does not fit the data. Fortunately, there are also other distributions. This is the Weibull distribution, and it is called a skewed distribution. A distribution like this is called skewed to the right, because the tail is to the right. The Weibull distribution is often used for data, like, throughput times, and processing times, because these are often skewed variables. Many values are relatively small, and some values are very high. The Weibull distribution can take various forms. There's a second distribution that is also often used for skewed data and that is a Lognormal distribution. And it looks like this. Let's go back through our example of throughput times. We saw that the normal distribution did not fit well. Let's have a look at the Weibull distribution. It fits better as the line follows the histogram more closely. Now the lognormal distribution. It also fits pretty good. It is the topic of the video entitled probability plots to determine which of these distributions will fit best. Summarizing, there are hundreds of different types of distributions, the normal distribution is seen most often. But the Weibull distribution and the lognormal distribution are relevant in Lean Six Sigma project as well. In the video probability plot, you will learn to find the best fitting distribution to your data.