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The Normal Distribution…

The Normal Distribution…. An important function that can’t be integrated (by elementary methods) and why we need numerical methods!. The Normal Distribution…. Z-values are used to calculate probabilities or estimate the fraction of a statistic that lies within a given range.

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The Normal Distribution…

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  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

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