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.

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CCSS.HSS.ID.A.4

Front

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

Back

Approximately 68%.

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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%.

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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%.

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CCSS.HSS.ID.A.4

Front

If the mean score of a test is 50 and the standard deviation is 10, what is the range for one standard deviation from the mean?

Back

40 to 60.

Front

How do you calculate the z-score?

Back

Z-score = (X - mean) / standard deviation.

Front

What does a z-score represent?

Back

A z-score indicates how many standard deviations an element is from the mean.

Front

In a normal distribution, what does it mean if a z-score is greater than 2?

Back

It means the value is more than 2 standard deviations above the mean, which is rare.

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CCSS.HSS.ID.A.4

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability, which equals 1.

Front

If a dataset has a mean of 100 and a standard deviation of 15, what is the probability of a value being less than 85?

Back

Approximately 16%.

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CCSS.HSS.ID.A.4