JAVA

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 results—true—but 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

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