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 of a distribution.

Front

How do you calculate a Z-score?

Back

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

Front

What does a Z-score of +1.25 mean?

Back

It means the score is 1.25 standard deviations above the mean.

Front

What is the empirical rule?

Back

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

Front

If the mean is 70 and the standard deviation is 5, what is the range for one standard deviation?

Back

The range is 65 to 75.

Front

What percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34%.

Front

What is the Z-score for a score of 80 if the mean is 70 and the standard deviation is 5?

Back

Z = (80 - 70) / 5 = +2.0.

Front

What is the probability of scoring above the mean in a normal distribution?

Back

50% of the scores fall above the mean.

Front

If a score is at the 95th percentile, what can be said about its Z-score?

Back

The Z-score is approximately +1.645.

Front

What does it mean if a Z-score is negative?

Back

It indicates that the score is below the mean.