Question

What does the central limit theorem require?

Answer 1

Central limit theorem

1. The central limit theorem states that if a large random sample is taken from a population of mean $\overline{X}$ and standard deviation $\sigma$, then the distribution of the sample means will be approximated to normal distribution.
2. The larger the sample size, the more it will be close to normal distribution.

The key aspects of the Central Limit Theorem are:

1. A sample size of $30$or more is considered a large sample and the theorem holds good.
2. The average means and standard deviation of the sample will be equal to that of the population.
3. A sufficiently large sample can predict the characteristics of a population.

Hence, central limit theorem requirement is explained.