The area from 0 to z under the Standard Normal Curve can be computed by the Calculus-generated expression:
A = (1/√(2π))∫(from t = 0 to t = z)e(-t squared/2)dt.
This Formula can be programmed into a Casio Programmable Calculator as (1/√(2π))∑(from n = 0 to n = ∞)((-1)n/(n!2n))[z(2n + 1)/(2n + 1)].
Running this program for z = 1.24 will yield A = 0.3925123029.
Running this program for z = 0.72 will yield A = 0.2642375022.
The Area between z =0.72 and z = 1.24 is then given as (0.3925123029 − 0.2642375022) or 0.1282748007 square units, ≈ 0.1283 square units.
Entering z = 0.72 and z = 1.24 as arguments into a Table of Proportions Of Area Under The Standard Normal Curve will give 0.3925 for z = 1.24 and 0.2642 for z = 0.72, which yield (0.3925 − 0.2642) or 0.1283 square units as the Area Under The Standard Normal Curve between z = 0.72 and z = 1.24.
