Explain the significance of Central Limit Theorem and how is

Explain the significance of \"Central Limit Theorem\" and how is the theorem applicable to inferential statistics. Explain the significance of the \"Chebyshev\'s Theorem\" and its application in statistics.

Solution

2a)

The central limit theorem is significant because it says that the sampling distribution of sample means is approximately normally distributed for a sufficiently large number of iterates.

Thus, this gives us the convenience of approximating the distirbution of sample means is normal even though we do not know the original distirbution of the data points themselves.

This is useful because we are usually concerned on the distribution of sample means (hence, giving us a chance to calculate things about the population mean), not the data points themselves.

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