Empirical Rule & Z-Scores

Front

What is a z-score?

Back

A z-score tells you how many standard deviations away from the mean a score lies.

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.

Front

If a distribution is normal, what can we say about the z-scores?

Back

Z-scores in a normal distribution can be used to determine the relative position of a score within the distribution.

Front

What is the empirical rule?

Back

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.

Front

How do you calculate a z-score?

Back

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

Front

What does a z-score of 0 indicate?

Back

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

Front

What does a positive z-score indicate?

Back

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

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the score is below the mean.

Front

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

Back

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

Front

If a woman's height has a mean of 63.6 inches and a standard deviation of 2.5 inches, what is the height of a woman with a z-score of 2.56?

Back

The height is 70 inches.