Z-Scores and Z-Score Table Flashcard

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

Front

What does a positive Z-Score indicate?

Back

A positive Z-Score indicates that the value is above the mean.

Front

What does a negative Z-Score indicate?

Back

A negative Z-Score indicates that the value is below the mean.

Front

What is the purpose of a Z-Score table?

Back

A Z-Score table provides the area (probability) to the left of a given Z-Score in a standard normal distribution.

Front

How do you find the area to the right of a Z-Score?

Back

To find the area to the right of a Z-Score, subtract the area to the left from 1.

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What is the empirical rule?

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, and 99.7% within three.

Front

What is the mean and standard deviation of SAT scores in 2014?

Back

Mean = 1497, Standard Deviation = 322.

Front

How do you find the probability of a range of values in a normal distribution?

Back

Calculate the Z-Scores for both values, find the corresponding areas in the Z-Score table, and subtract the smaller area from the larger area.

Front

What is the significance of the standard normal distribution?

Back

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, used for standardizing scores.