A Derivation of the Equation of the Normal Probability Curve

y = ƒ(#). On the positive side of the ^-plane take the curve lying on this cylindrical surface and satisfying the condition z = P(x) ; on the other side take the curve lying on the cylindrical surface and satisfying the condition z = — N(x). We thus intercept between two curves a part of the cylindrical surface for which x is on (ab). It is not difficult to form a fair intuitive notion of this portion of the surface since P(x) and N(x) are both monotonie non-decreasing. Then the integral (2) is the "area" of the part of this bounded cylindrical surface lying on the positive side of the ay-plane minus the "area" of that part lying on the other side.