Area Estimation

 

We will estimate area under the curve using what is essentially a Riemann Sum, which says that if you divide the area into a series of rectangles and calculate their areas, you can estimate the area under a curve; the more rectangles, the better the estimation. We will use integers as our x values, calculate corresponding y values, and sum those up to get an area estimation. We could use smaller values and get better resultstruebut we will also be drawing the curve, so these integers fit nicely into the x values we will use for drawing.One key interest is in demonstrating that the typical rules of thumb for normal distributions are correct. We expect about 68% of the area to be within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Our calculations should verify that