Empirical Rule

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution, approximately 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.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of scores are less than the mean in a normal distribution?

Back

50% of scores are less than the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

If the mean is 70 and the standard deviation is 5, what is the interval that contains approximately 95% of the data?

Back

The interval is from 60 to 80.

Tags

CCSS.HSS.ID.A.4

Front

In a normal distribution, what percentage of data falls between the mean and one standard deviation above the mean?

Back

34% of the data falls between the mean and one standard deviation above the mean.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data around the mean.

Front

If a normal distribution has a mean of 15 and a standard deviation of 3, what is the interval that contains approximately 68% of the data?

Back

The interval is from 12 to 18.

Tags

CCSS.HSS.ID.A.4

Front

In a normal distribution, what percentage of data falls within three standard deviations of the mean?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

What is the z-score formula?

Back

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

Front

If the mean is 24 and the standard deviation is 4, what percentage of ACT scores are between 20 and 28?

Back

68% of ACT scores are between 20 and 28.

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if a data point has a z-score of 0?

Back

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