What is a z Statistic?

The z Distribution is a standardized random sampling distribution of X-values, where X is a random variable drawn from a Normal Distribution. The z statistic reflects the the number of standard deviations or standard errors, X is away from the mean. The generic form of the z statistic calculation is:

zscoreCalc

Where:

X is the value of interest,

Mu is the mean, and

sigma is the standard deviation or standard error.

The z Distribution has a mean of zero and a standard deviation of one. The equation defining the z distribution curve is:

zDistCurve

The z distribution has the following shape.

ZDistPict