# Let’s go for basics first

## Standard Normal Distribution

`                      z = (X — μ) / σ`

# Assumptions Behind the Central Limit Theorem

1. The data must follow the randomization condition. It must be sampled randomly.
2. Samples should be independent of each other. One sample should not influence the other samples.
3. Sample size should be no more than 10% of the population when sampling is done without replacement.
4. The sample size should be sufficiently large. When the population is skewed or asymmetric, the sample size should be large. If the population is symmetric, then we can draw small samples as well.

# Code in Python

`from numpy.random import seedfrom numpy.random import randintfrom numpy import meanimport matplotlib.pyplot as plt# seed the random number generatorseed(1)# generate a sample of women's weightsweights = randint(50, 80, 40)print(weights)print('The average weight is {} kg'.format(mean(weights)))`
`means = [mean(randint(50, 80, 40)) for _i in range(1000)]# plot the distribution of sample meansplt.hist(means)plt.show()print('The mean of the sample means is {}'.format(mean(means)))`

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