Finding z-scores & using z-tables

A z-score indicates how many standard deviations an element is from the mean of a data set.

The formula for calculating a z-score is: $$z = \frac{(X - \mu)}{\sigma}$$ where X is the value, \mu is the mean, and \sigma is the standard deviation.

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

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

A negative z-score indicates that the data point is below the mean.

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 standard deviations, and 99.7% within three standard deviations.

The mean of a normal distribution is the central value around which the data is distributed.

The standard deviation measures the dispersion or spread of the data points around the mean.

A z-score of -1.25 indicates that the data point is 1.25 standard deviations below the mean.

Approximately 15.87% of values are less than a z-score of -1 in a normal distribution.