Normal Distributions and Z-scores

Front

What is a normal distribution?

Back

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.

Front

What is the mean (μ) in a normal distribution?

Back

The mean (μ) is the average of all data points in a normal distribution, representing the center of the distribution.

Tags

CCSS.HSS.ID.A.2

CCSS.6.SP.B.5D

Front

What is standard deviation (σ)?

Back

Standard deviation (σ) measures the amount of variation or dispersion of a set of values, indicating how much the values deviate from the mean.

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 does a z-score of 0 indicate?

Back

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 positive z-score indicate?

Back

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

Front

What does a negative z-score indicate?

Back

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

Front

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

Back

Approximately 68% of the data falls within one standard deviation (μ ± σ) of the mean.

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CCSS.HSS.ID.A.4

Front

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

Back

Approximately 95% of the data falls within two standard deviations (μ ± 2σ) of the mean.

Tags

CCSS.HSS.ID.A.4

Front

What is the empirical rule?

Back

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

Tags

CCSS.HSS.ID.A.4