Normal Distribution + Z-score

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What is a Normal Distribution?

Back

A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where most of the observations cluster around the central peak (mean), and probabilities for values further away from the mean taper off equally in both directions.

Front

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 by subtracting the mean from the value and then dividing by the standard deviation.

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How do you calculate a Z-score?

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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 positive Z-score indicate?

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A positive Z-score indicates that the value is above the mean.

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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.

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What is the Empirical Rule?

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

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

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Approximately 68%.

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What percentage of data falls within two standard deviations of the mean in a normal distribution?

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Approximately 95%.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

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Approximately 99.7%.