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------------------------------------------------ What significance do the values 68, 95, and 99.7 have with regard to normal distributions? Include a diagram.

In a normal distribution, which is symmetrical and bell-shaped, these percentages hold true regardless of the specific values of the mean and standard deviation. This rule provides a rough guideline for understanding the spread and distribution of data in a normal distribution.

The values 68, 95, and 99.7 are significant in the context of normal distributions because they represent approximate percentages of data within specific intervals around the mean. This concept is known as the "68-95-99.7 rule" or the "empirical rule."

Here is a diagram that illustrates the 68-95-99.7 rule:

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99.7%

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95%

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68%

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Mean

According to the rule:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

In a normal distribution, which is symmetrical and bell-shaped, these percentages hold true regardless of the specific values of the mean and standard deviation. This rule provides a rough guideline for understanding the spread and distribution of data in a normal distribution.

Please note that the diagram is a representation of the rule and the percentages are approximate. In reality, the exact percentages may vary slightly depending on the specific characteristics of the distribution.

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