Answer :
Final answer:
The 68-95-99.7 rule or Empirical Rule is applied to a normal distribution (bell-shaped and symmetric). It states that within one, two, and three standard deviations from the mean, you can expect to find 68%, 95%, and 99.7% of the values, respectively.
Explanation:
The 68-95-99.7 rule, also known as the Empirical Rule, applies to a bell-shaped and symmetric distribution, commonly termed as a normal distribution. This rule implies that about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations and approximately 99.7% falls within three standard deviations.
For instance, if we have a mean (µ) of 20 and a standard deviation (σ) of 10, then:
- About 68% of values will lie in the range (µ-σ) to (µ+σ), which means between 10 (20-10) and 30 (20+10).
- Close to 95% of values would be between 0 (20-2*10) and 40 (20+2*10).
- Almost 99.7% of values are expected between -10 (20-3*10) and 50 (20+3*10).
You need a z-table to validate these percentages because the z-table links z-scores (number of standard deviations from the mean) with their associated percentages.
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