Google Classroom
GeoGebraGeoGebra Classroom

Approximating Area Under the Standard Normal Distribution

How does the computer calculate the area underneath the standard normal distribution function, N(0, 1)? This worksheet shows the secret. The method consists of embedding a shape that the formula for the area is known and using that to approximate the needed area under the function. In this case the shape chosen is a rectangle. I have created two different scenarios. One which is always an underestimate (darker rectangles, lower sum value) of the total area. Notice that the rectangle height is determined by the location on the function itself. The other method uses a rectangle but this time the total area is always an overestimate (upper sum value) of the actual area. Use the slider to increase or decrease the number of rectangles. As the number of rectangles increases the estimation becomes better as demonstrated by the difference between the upper and lower sum. You can move the points A, B, to find the area for different sections of the standard normal distribution function.