Normal Distribution -empirical rule

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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 is the Empirical Rule?

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

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CCSS.HSS.ID.A.4

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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%.

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CCSS.HSS.ID.A.4

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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%.

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CCSS.HSS.ID.A.4

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

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Approximately 99.7%.

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CCSS.HSS.ID.A.4

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If the mean GPA is 3.2 and the standard deviation is 0.3, what is the range for one standard deviation?

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The range is 2.9 to 3.5.

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If the mean is 75 and the standard deviation is 7, what is the range for one standard deviation?

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The range is 68 to 82.

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How do you calculate the z-score?

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The z-score is calculated using 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 tell you?

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A z-score indicates how many standard deviations an element is from the mean.

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If a student scores 82 on a test with a mean of 75 and a standard deviation of 7, what is the z-score?

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The z-score is 1.0.