What’s the normal distribution? Why do we care about it?
The normal distribution is a continuous probability distribution whose probability density function takes the following formula:
where μ is the mean and σ is the standard deviation of the distribution.
The normal distribution derives its importance from the Central Limit Theorem, which states that if we draw a large enough number of samples, their mean will follow a normal distribution regardless of the initial distribution of the sample, i.e the distribution of the mean of the samples is normal. It is important that each sample is independent from the other.
This is powerful because it helps us study processes whose population distribution is unknown to us.