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Answer :
Final answer:
The 68-95-99.7 rule or the Empirical Rule is a statistical rule that states that for any normal distribution, approximately 68% of data points will fall within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations. The rule provides a fast estimate of the distribution of data in a bell-curve.
Explanation:
The Empirical Rule or the 68-95-99.7 rule is applied when data points follow a normal distribution having mean 'µ' and standard deviation 'σ'. Here's how to use the rule:
- About 68% of data fall within one standard deviation from the mean, i.e., between µ-σ and µ+σ.
- Approximately 95% of data points fall within two standard deviations, i.e., between µ-2σ and µ+2σ.
- Nearly 99.7% of data fall within three standard deviations, i.e., between µ-3σ and µ+3σ.
Using this information, if a statistics student has to apply the rule, they can calculate the mean and the standard deviation to find the range that would contain 68%, 95%, and 99.7% of their data. For example, assuming a mean of 60 (N(60, 5.477) - where 5.477 is the standard deviation), about 68% of the students would be expected to score between 54.523 and 65.477.
This rule is fundamental in statistical inference and provides a quick approximation of the distribution of data in a bell-structured curve, commonly seen in nature.
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