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.

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.

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.

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.

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.