Central limit theorem for means

Regardless of the distribution of the data, the central limit theorem (CLT), among other benefits, allows us to assume normality of the sampling distributions of metrics that we often examine in A/B testing such as means, sums, proportions, standard deviations, and percentiles. Statistical significance tests that assume normality can therefore be easily applied to such scenarios in order to make solid conclusions about our experiments.

The goal of this exercise is to demonstrate how the CLT applies to various distributions and appreciate its power.

The following has been loaded for you:

• the checkout DataFrame
• pandas as pd
• numpy as np
• matplotlib as plt
• seaborn as sns