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, approximately 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

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What percentage of data lies within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data.

Front

What percentage of data lies within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data.

Front

What percentage of data lies beyond three standard deviations from the mean in a normal distribution?

Back

Approximately 0.3% of the data.

Front

How do you calculate the z-score for a given value?

Back

Z-score is calculated using the formula: z = (X - μ) / σ.

Front

If the mean of a dataset is 50 and the standard deviation is 10, what is the z-score for a value of 70?

Back

The z-score is 2.0.

Front

What does a z-score of 0 indicate?

Back

A z-score of 0 indicates that the value is exactly at the mean.

Front

In a normal distribution, what does it mean if a z-score is positive?

Back

A positive z-score indicates that the value is above the mean.