Chapter 5 - Central limit theorem

Central limit theorem

The mean of a large random sample taken from any random variable is always approximately normally distributed, regardless of the distribution of the original random variable

As the population size increases, the variance decreases, hence making the normal distribution curve smoother

When to use the central limit theorem

When the population size is large

Trials must be independent of each other

X̄ = the mean of X

~ = the approximately normal distribution of X̄

μ = the mean

σ² = the variance

n = population size

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