Normal Distributions

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution that is symmetrical around its mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What are the parameters of a normal distribution?

Back

The parameters of a normal distribution are the mean (μ) and the standard deviation (σ).

Tags

CCSS.6.SP.A.3

Front

What does the mean (μ) represent in a normal distribution?

Back

The mean (μ) represents the average value of the data set and is the center of the normal distribution.

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CCSS.HSS.ID.A.2

CCSS.6.SP.B.5D

Front

What does the standard deviation (σ) indicate in a normal distribution?

Back

The standard deviation (σ) indicates the spread or dispersion of the data points around the mean.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the z-score?

Back

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.

Front

What is the significance of a z-score of 0?

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A z-score of 0 indicates that the data point is exactly at the mean of the distribution.

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What does a negative z-score indicate?

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A negative z-score indicates that the data point is below the mean.

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What does a positive z-score indicate?

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A positive z-score indicates that the data point is above the mean.

Front

What percentage of data lies within ±1 standard deviation in a normal distribution?

Back

Approximately 68% of the data lies within ±1 standard deviation from the mean.

Tags

CCSS.HSS.ID.A.4