Here, I wanted to give the opportunity for others to compare my distribution to the Normal Curve.
1) The red curve is the Normal Curve
2) The two sliders represent the area from both distributions together.
3) Move the sliders around and then match the numbers to see how the areas equal each other.
4) The Standard Deviations are Constant here; They are offset to each other in order for their curves to match.
5) The Normal Curve is set: Standard Deviation = 1
6) RV Sigma is set: Standard Deviation = 1.1748 and this is the offset from the Normal Curve which I have held constant here so as to have equivalent probabilities !!
7) Check against probability Calculator.

Move the Sliders to different positions; compare to probability calculator