Given any data set, the z-score for any given data point within the data set is the number of standard deviations that data point is above the mean.
If we have the mean 
and standard deviation 
of a data set, we can calculate the z-score 
of any given data point 
with the following formula
We might also want to go in the opposite direction, we might want to know what data value would produce a given z-score. To do this, we merely have to solve the above equation for x
and plug in 
and 
