Normal distribution curve area?

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SUMMARY

The discussion centers on calculating the area under the normal distribution curve for specific sigma values, particularly 2.5 sigma. It confirms that while common sigma values like 1, 2, and 3 can be easily referenced (68.3%, 95%, and 99.7% respectively), calculating the area for 2.5 sigma requires numerical integration or the use of pre-existing tables. Tools such as Wolfram Alpha, Mathematica (MMA), and Matlab are mentioned as effective for performing definite integrals, but no simple algorithm exists for this specific calculation.

PREREQUISITES
  • Understanding of normal distribution and sigma values
  • Familiarity with numerical integration techniques
  • Basic knowledge of statistical software like Matlab and Mathematica
  • Experience with probability theory and integrals
NEXT STEPS
  • Explore numerical integration methods in Matlab
  • Learn how to use Wolfram Alpha for statistical calculations
  • Study the properties of the standard normal distribution
  • Investigate advanced statistical software options for probability analysis
USEFUL FOR

Statisticians, data analysts, and anyone involved in probability theory who needs to compute areas under the normal distribution curve.

Scott S
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Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value?
For example;
3 sigma = 99.7
2 sigma = 95
1 sigma = 68.3
Now suppose I wanted to know 2.5 sigma without a table.
 
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Wolfram Alpha, MMA, Matlab, and other programs are pretty good at definite integrals.
 
No, there isn't. The standard normal distribution probability that "z< a" is \frac{1}{\sqrt{2\pi}}\int_{-\inf}^a e^{-\frac{x^2}{2}} dx. That cannot be integrated in terms of elementary functions so either do a numerical integration or use a table (which was developed by numerical integrations).
 

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