Ch.5- Empirical Rule and Z-Scores

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What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation (σ) of the mean (μ), about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

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What is a Z-Score?

Back

A Z-Score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated as Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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How do you calculate the Z-Score for a given value?

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To calculate the Z-Score, use the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does a Z-Score of 0 indicate?

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A Z-Score of 0 indicates that the value is exactly equal to the mean of the distribution.

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What does a negative Z-Score indicate?

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A negative Z-Score indicates that the value is below the mean of the distribution.

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What does a positive Z-Score indicate?

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A positive Z-Score indicates that the value is above the mean of the distribution.

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If a test score is 2 standard deviations above the mean, what is the Z-Score?

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The Z-Score would be +2.

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What percentage of data falls below a Z-Score of 1 in a normal distribution?

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Approximately 84% of the data falls below a Z-Score of 1.

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What percentage of data falls between Z-Scores of -1 and +1?

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Approximately 68% of the data falls between Z-Scores of -1 and +1.

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How do you find the percentage of students scoring below a certain score using the Z-Score?

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Calculate the Z-Score for the score, then use the Z-Score table (or calculator) to find the corresponding percentage.