Z-Scores Given the Area

Front

What is a Z-score?

Back

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.

Front

How do you calculate a Z-score?

Back

Z-score = (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 0 indicate?

Back

A Z-score of 0 indicates that the data point is exactly at the mean.

Front

What does a positive Z-score indicate?

Back

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

Front

What does a negative Z-score indicate?

Back

A negative Z-score indicates that the data point is below the mean.

Front

What is the empirical rule in statistics?

Back

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

Front

What is the cumulative area in relation to Z-scores?

Back

The cumulative area represents the probability that a value will fall below a given Z-score in a standard normal distribution.

Front

How do you find the Z-score corresponding to a given cumulative area?

Back

You can use Z-tables or statistical software to find the Z-score that corresponds to a specific cumulative area.

Front

What is the Z-score for the 90th percentile?

Back

The Z-score for the 90th percentile is approximately 1.28.

Front

If the mean is 25 and the standard deviation is 7, what is the value of x for a Z-score of -2.2?

Back

x = μ + (Z * σ) = 25 + (-2.2 * 7) = 9.6.