Normal Distributions and Z Scores

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What is a normal distribution?

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A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal. It is defined by its mean (μ) and standard deviation (σ).

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What is a z-score?

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Front

How do you calculate a z-score?

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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 of the data set.

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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 of the data set.

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What is the empirical rule in relation to normal distributions?

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

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CCSS.HSS.ID.A.4

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How do you find the area under the normal curve for a given z-score?

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To find the area under the normal curve for a given z-score, refer to a z-table, which provides the cumulative probability associated with z-scores.

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CCSS.HSS.ID.A.4

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What is the mean of a normal distribution?

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The mean of a normal distribution is the central value around which the data is distributed, denoted as μ.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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What is the standard deviation of a normal distribution?

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The standard deviation of a normal distribution, denoted as σ, measures the dispersion or spread of the data around the mean.

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How do you interpret a z-score of 2.34?

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A z-score of 2.34 indicates that the value is 2.34 standard deviations above the mean.