Normal distribution and Empirical Rule

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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 of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

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 of the distribution.

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 mean in a normal distribution?

Back

The mean is the average of all data points and is the center of the normal distribution.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

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

What percentage of data falls between two standard deviations of the mean?

Back

Approximately 95% of the data falls between two standard deviations of the mean.