Let's talk about the famous Normal Distribution. As it is used so often, I want to explain some useful properties to you. This is the Normal Distribution, it is symmetrical and it looks a little bit like a bell. That is why it is also called the Bell-shaped distribution. Carl Friedrich Gauss is often associated with this distribution and its form. He was born in Germany in 1777 and made significant contributions to the Normal Distribution. That is why the Normal Distribution is also often called the Gauss curve. A Normal Distribution has two parameters that determine the shape of its distribution. The first parameter is the location parameter which determines the midpoint. This is denoted by mu, which is the location or mean. The second parameter describes the shape of the distribution and is known as the dispersion parameter, denoted by sigma. And it determines the spread of the distribution. The location of a Normal Distribution can be changed by manipulating mu. Can you tell which of these three Normal Distribution will have the highest mu? It is the distribution that is situated most to the right, that has the largest mu. It is also possible to change the scale of the distribution by tweaking the sigma. Can you tell which of these three Normal Distributions shows the largest spread, the largest sigma? Well, it is the distribution where the graph is flattened out most. The Normal Distribution has a few properties that are often used. A variable that is normally distributed will always be, for 68% of the time, in between the new mu plus 1 sigma and minus 1 sigma. Equivalently, 95% of the population will be in between plus and minus 2 times sigma. You might know this rule from the 95% confidence intervals. 99% of the population will be in between the mean and plus 2.5 times the sigma and minus 2.5 times the sigma and 99.7 % will be in between plus and minus 3 times sigma. These can be used as rules of thumb for calculations of a variable that is normally distributed. Let's illustrate how to use these rules of thumb. I tested the caffeine percentage in coffee, remember? And the caffeine percentage follows a Normal Distribution and I found a mean of 0.083 and a standard deviation of 0.016. Now using these properties of the Normal Distribution, we can say that 68% of all the coffee that is produced will have a caffeine percentage between 0.067 and 0.099. 95% of all produced coffee will have a caffeine percentage between 0.051 and 0.115. 99% of all produced coffee will have a caffeine percentage between 0.043 and 0.123 and finally, 99.7% will be in between 0.035 and 0.131. Summarizing, though Normal Distribution occurs very often. The Normal Distribution has some interesting properties which facilitate rules of thumb to compute relevant percentages.