Normal Distribution

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.

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What is the shape of a normal distribution curve?

Back

The shape of a normal distribution curve is called a bell curve.

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What is the Empirical Rule?

Back

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

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CCSS.HSS.ID.A.4

Front

What does the mean represent in a normal distribution?

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

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation indicates the amount of variation or dispersion of a set of values. A smaller standard deviation means the data points are closer to the mean.

Front

If the mean is 38 and the standard deviation is 4, what is the z-score for a value of 34?

Back

The z-score is calculated as (X - mean) / standard deviation = (34 - 38) / 4 = -1.

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What percentage of data falls below the mean in a normal distribution?

Back

50% of the data falls below the mean in a normal distribution.

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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 value 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 value is below the mean.