What is the Normal Distribution?

The normal distribution is a continuous probability distribution that has a bell-shaped, it is also known as the Gaussian function.

Technically, the normal curve has a formula:

This formula results in the following graphs, depending on the mean and standard deviation:

No matter what, the normal curve has a bell-shape and is symmetric about its mean.

When a variable X is from a normal distribution, we say this in "stat-speak" by using the following notation:
This says "X follows a Normal distribution with mean of μ and standard deviation of σ." The X and N will always stay the same, but the mean and standard deviation will be replaced by whatever values they are.

Next: We also know the approximate areas under the curve for any normal distribution using The Empirical Rule.