Normal Distribution and Empirical Rule

Front

What is a normal distribution?

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A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

Front

What is the empirical rule?

Back

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

Front

How do you calculate a z-score?

Back

Front

What does a z-score of 0 indicate?

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A z-score of 0 indicates that the value is exactly equal to the mean of the distribution.

Front

What percentage of data falls below a z-score of 1?

Back

Approximately 84.13% of data falls below a z-score of 1 in a normal distribution.

Front

If the mean is 50 and the standard deviation is 5, what is the z-score for 48?

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Front

Using the empirical rule, what percent of values are less than one standard deviation below the mean?

Back

Approximately 16% of values are less than one standard deviation below the mean.

Front

What is the z-score for a value of 30, given the data set {23, 15, 4, 11, 1, 29, 3, 17}?

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Front

If the mean is 16 and the standard deviation is 4, what is the z-score for 11?

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