Area Under the Normal Curve using Integration . The table can be used to find a z value given and area, or and area given a z value. The area under the normal curve to the left of z = 1.53 would be graphically represented like this: The vertical line dividing the black shaded region from the white un-shaded region is z = 1.53. It is also called Gaussian distribution. The probability of a continuous normal variable X found in a particular interval [a, b] is the area under the curve bounded by `x = a` and `x = b` and is given by `P(a