Question

Question 1: How is the empirical distribution related to the normal distribution?

Question 2: How is the normal distribution related to the standard normal distribution?

Question 3: What is the importance of the Central Limit Theorem?

Answer 1

Answer 1) The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean, 68% of data falls within the first standard deviation from the mean, 95% fall within two standard deviations, 99.7% fall within three standard deviations.

Answwer 2) Any point (x) from a normal distribution can be converted to the standard normal distribution (z) with the formula z = (x-mean) / standard deviation.

Answer 3) The central limit theorem tells us exactly what the shape of the distribution of means will be when we draw repeated samples from a given population. Specifically, as the sample sizes get larger, the distribution of means calculated from repeated sampling will approach normality.

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