Here, I have used the Equation for Z percentiles to obtain the Normal Probabilities. ( I posted this really so you can see this relationship ) I can table the " i " values and use this to calculate Normal Probabilities.
( Type in std. or z values, z=1/z into sigma boxes )
You can get any probability by changing "Sum ' i ' " while leaving " n " at 5000. ( The two equations of interest, are equation " i " and capital " I " )
I set equation of the area of " i " to the area at 1 std. of the Normal Curve which
gave me the purple Line.
Even though the area of the Green Curve is not shown, it always equals the value of the Standard Deviation of the Normal Curve. ( I have a separate box for the standard deviation )
I know posting this seems to be redundant, but it is not; This is another way to solve normal probabilities using a simple equation. This is a continuous work in progress.
The Range on " i " is from ( 1 to 225.5 ) and " i " will give you all the Z values from ( .01 to 4.5 ) as well as all probabilities of the Area of the normal curve. ( You will need great patience to dial in the numbers but you can, in fact, obtain all values using " i , " while leaving " n " at 5000.