The Central Limit Theorem

[Deede]

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How does one calculate the sampling distribution of X when you have the random sample of size n, mean, and standard deviation. I would appreciate any help that I can get.

 

[DrPhil]

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How does one calculate the sampling distribution of X when you have the random sample of size n, mean, and standard deviation. I would appreciate any help that I can get.

Suppose you know the mean and the standard deviation of the "population" distribution - but not necessarily the shape of the distribution. The central limit theorem states that if you take samples of size n from the population, the distribution of sample means will approach a Normal distribution as n gets large. Further, the mean of the sample means will equal the population mean, and the standard deviation of the sample means will be the population standard deviation divided by $\displaystyle \sqrt{n}$.

Population:................... $\displaystyle \mu,\;\;\sigma$

Mean of sample of size $\displaystyle n$: $\displaystyle \mu, \;\;\dfrac{\sigma}{\sqrt{n}}$

 

[Deede]

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How does one calculate the sampling distribution of X when you have the random sample of size n, mean, and standard deviation. I would appreciate any help that I can get.

Thank you Dr. Phil. I understand it now.

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