Normal Distributions

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What is a normal distribution?

Back

A normal distribution is a continuous 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 are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of data falls within one standard deviation of the mean.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average value of the dataset and is located at the center of the normal distribution curve.

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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 measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points are closer to 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 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?

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

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CCSS.HSS.ID.A.4

Front

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

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

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CCSS.HSS.ID.A.4

Front

If the mean shelf life of a product is 12 days and the standard deviation is 3 days, what percent of products last between 12 and 15 days?

Back

34% of the products last between 12 and 15 days.

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CCSS.HSS.ID.A.4

Front

In a normal distribution, what is the symbol for the mean?

Back

The symbol for the mean is μ.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

In a normal distribution, what is the symbol for the standard deviation?

Back

The symbol for the standard deviation is σ.