Normal Distributions

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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 are the key characteristics of a normal distribution?

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1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of the data falls within one standard deviation of the mean.

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What is the mean in a normal distribution?

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The mean is the average of all data points in a normal distribution and is the center point of the distribution.

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CCSS.6.SP.B.5D

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What is the standard deviation in a normal distribution?

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The standard deviation measures the amount of variation or dispersion of a set of values in a normal distribution.

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What is a z-score?

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A z-score indicates how many standard deviations a data point is from the mean of the distribution.

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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.

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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.

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

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

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CCSS.HSS.ID.A.4

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What is the empirical rule?

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The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

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CCSS.HSS.ID.A.4