Normal Distribution 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 does the Z-score represent?

Back

The Z-score represents the number of standard deviations a data point is from 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.

Tags

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 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?

Back

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

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CCSS.HSS.ID.A.4

Front

What is a positive Z-score?

Back

A positive Z-score indicates that the observed value is above the mean.

Front

What is a negative Z-score?

Back

A negative Z-score indicates that the observed value is below the mean.

Front

How do you calculate a Z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

If the mean is 15 and the standard deviation is 3, what is the range for 99.7% of the data?

Back

The range is from 6 to 24.

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if a Z-score is 0?

Back

A Z-score of 0 means the observed value is exactly at the mean.