Normal Distribution and Z scores

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What is a normal distribution?

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A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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

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

Tags

CCSS.HSS.ID.A.4

Front

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

Back

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

Tags

CCSS.HSS.ID.A.4

Front

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

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

Tags

CCSS.HSS.ID.A.4

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, expressed in terms of standard deviations.

Tags

CCSS.HSS.ID.A.4

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If a z-score is +1, what does it indicate?

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A z-score of +1 indicates that the value is one standard deviation above the mean.

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If a z-score is -1, what does it indicate?

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A z-score of -1 indicates that the value is one standard deviation below the mean.

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What does a positive z-score represent?

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A positive z-score represents an observed value that is above the mean.

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What does a negative z-score represent?

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A negative z-score represents an observed value that is below the mean.

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How do you calculate a z-score?

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Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.