There are 10 black stones and 10 white stones in your pocket. What is the distribution of the number of black stones when I take out 10 randomly?
Binomial distribution
When you take a stone out of your bag, the result will be either white or black. A trial in which the result is divided only two like this is called a Bernoulli trial. When this Bernoulli trial is repeated n times independently, the resulting distribution is called a ‘binomial probability distribution’.
The results show that the highest probability is getting 5 each of white and black. The ‘binomial distribution’ resembles a ‘normal distribution’ if the probability is constant and the number of trials is sufficiently large.
Normal distribution
Gauss in Germany has researched how much error is made when doing various experiments, and the result is announced as ‘law of error.’ The distribution curve of this ‘law of error’ is ‘normal distribution.’
The normal distribution is the most commonly used distribution curve used as a statistical model.
(Standard Deviation σ = 1)
Most phenomena occurring in nature are similar to normal distribution curves. For example, the height, weight, and IQ of a student in a classroom are known to form a normal distribution curve.
The average number of students is the highest, and the further away from the average, the fewer the number of students.
Distribution of male and female height between 25 and 29 (http://sizekorea.kats.go.kr/)
Note that the normal distribution curve is merely mathematically derived. It is used as a mathematical model only if it is suitable for describing realistic data.