Normal Distribution and Z scores

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 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 within two standard deviations of the mean in a normal distribution?

Back

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

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7% of the data falls within three standard deviations of the mean.

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.

Front

If a z-score is +1, what does it indicate?

Back

A z-score of +1 indicates that the value is one standard deviation above the mean.

Front

If a z-score is -1, what does it indicate?

Back

A z-score of -1 indicates that the value is one standard deviation below the mean.

Front

What does a positive z-score represent?

Back

A positive z-score represents an observed value that is above the mean.

Front

What does a negative z-score represent?

Back

A negative z-score represents an observed value that is below 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.