The Independent Z Distribution
This is an Independent Z Distribution with the Blue area of the Normal equal to 4.5 and .01 at each end of the Standard Deviations of : .2222 and 100 respectively. ( Blue Sigma Box ) N operates the Curvature of the Z Distribution p(x). Sigma 1 operates the Normal Distribution ( Purple Sigma Box ) Sigma operates the Blue distribution as well as the Standard Deviation Distribution a(x). I multiplied the Blue area by 10 so the Decimal spits out the right number: It is only a reference area that has each specific Z value of the Normal Probability, so there is some way to compare areas.
Type in different values to see the independence of the Distributions.