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According to the Empirical Rule (also called the 68-95-99.7 rule), if the data form a "bell-shaped curve" (normal distribution), approximately what percent of the observations will be contained within one standard deviation of the mean?

Answer :

Final answer:

The Empirical Rule, or the 68-95-99.7 rule, indicates that in a normal or bell-shaped distribution, about 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three.

Explanation:

The Empirical Rule, also known as the 68-95-99.7 rule, applies to a distribution that is shaped like a bell curve. In other words, it applies to the normal distribution scenario.

In a normal distribution, the rule indicates that approximately:

  • 68% of the data falls within one standard deviation from the mean
  • 95% falls within two standard deviations,
  • and finally, about 99.7% falls within three standard deviations.

This rule is extremely useful in statistics when making predictions about a data set without having to actually calculate said data.

For example, if we know that a set of data has a normal distribution and we know the standard deviation, we can predict that about 68% of data observed will fall within one standard deviation of the mean. Similarly, approximately 95% of data will be covered within two standard deviations and almost entire data around 99.7% will be covered within three standard deviations according to the Empirical Rule.

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