Equations of the Z Distribution
These are the equations that make everything work. ( If you look at the list of numbers in the left side pane below the equations, you will see the Z vales go from .01 to 4.5 ,, which gives a standard deviations of 100.00 to .2222 ) The two Red Lines were calculated by taking the area of the large Normal Distribution and Dividing that by the Area of the my Standard Deviation equation: (Normal area)(/RV'S STD.) - Standard Deviation and (RV'S STD.)/(Normal area) - Z Value Line ; Which subsequently gives the Standard Deviation and the Z line Values, in proportion to, the Normal Curve in relation to the Z Distribution. a(x) is my Standard Deviation of the Normal Curve, Notice how it peaks at the top of the Z Distribution. Click in the left pane to activate or de-activate equations There are three relationships of Z/S and S/Z happening at once. The RED Z/S S/Z relationship- vertical , The Powder Blue Z/S S/Z relationship- horizontal, and The Slider with Z/S S/Z with RV'S Sigma Distribution which is also a horizontal relationship.
please see the equations above.