1. The Normal Distribution…
An important function that can’t be integrated (by elementary methods) and why we need numerical methods!

2. The Normal Distribution…
Z-values are used to calculate probabilities or estimate the fraction of a statistic that lies within a given range.
For example…. In a Math 205 Midterm exam the average score was 65% and the standard deviation was 10%. Estimate the fraction of the class that scored higher than 85%.

3. Where do z-values come from?
Easiest way is to numerically integrate

4. Numerical Integration Methods
Trapezoidal – approximate the function by a series of trapezoids
Simpson’s Method – approximate the function by a series of parabolas!
Error
Simpson’s Rule is very robust and an often used numerical scheme