- more mass in the center
- it has a spread that approaches zero but never touches it
- it resembles a lot of phenomena in real life
You can use Cumulative density function to calculate probability.
It is common to scale a normal so the mean is at zero and the variance is 1. That is called a standard normal distribution.
Central limit theorem
The normal is important because it appears even when a distribution is normal. One example is the central limit theorem where we find that even when values in a population are eavenly distributed the mean of a random sample takes the shape of a normal distribution.
This is important because we use this to establish when a sample size is enough. If it satisfies the central limit theorem then we have enough samples.