Normal Distribution

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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.

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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 located at the center of the distribution curve.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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What is the standard deviation in a normal distribution?

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The standard deviation is a measure of the amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

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What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

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Approximately 68% of the data falls within 1 standard deviation of the mean.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

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Approximately 95% of the data falls within 2 standard deviations of the mean.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

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Approximately 99.7% of the data falls within 3 standard deviations of the mean.

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CCSS.HSS.ID.A.4

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What is the total area under the normal distribution curve?

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The total area under the normal distribution curve is equal to 1.

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What does it mean if a data set is normally distributed?

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If a data set is normally distributed, it means that the data follows a pattern where most values cluster around the mean, and the probabilities of values further from the mean decrease symmetrically.

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CCSS.6.SP.A.3

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What is the empirical rule in statistics?

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

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CCSS.HSS.ID.A.4

Front

How does the normal distribution relate to the z-score?

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The z-score indicates how many standard deviations an element is from the mean. In a normal distribution, z-scores can be used to determine the probability of a value occurring.

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CCSS.HSS.ID.A.4