Z SCORES & EMPIRICAL RULE

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It is calculated as Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does the Empirical Rule state?

Back

The Empirical Rule states that for a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

If a score is 2 standard deviations below the mean, what is its Z-score?

Back

The Z-score is -2.00.

Front

What percentage of scores lie between the mean and 1 standard deviation above the mean in a normal distribution?

Back

34% of scores lie between the mean and 1 standard deviation above the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate a Z-score?

Back

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

Front

What is the Z-score for Gonzalo's score of 87 if the class average is 82 and the standard deviation is 4?

Back

Gonzalo's Z-score is +1.25.

Front

In a normal distribution, what percent of values lie below the mean?

Back

50% of values lie below the mean.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of ACT scores are between 20 and 28 if the mean is 24 and the standard deviation is 4?

Back

68% of ACT scores are between 20 and 28.

Tags

CCSS.HSS.ID.A.4

Front

What is the Z-score for a score that is exactly at the mean?

Back

The Z-score is 0.00.

Front

What does a positive Z-score indicate?

Back

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