Grand Social Law ◾ 229
3. Why does the bell curve perfectly fit all the different variance metrics such as
effort variance, schedule variance, and size variance?
4. Name the famous mathematicians and scientists who have contributed to the
development of the bell curve.
5. Mention three important applications of the bell curve.
Exercises
1. In the context of a bell curve with mean = 7 and standard deviation = 6, find
the z score of a data point 25.
2. Dr. Shewhart prescribed three sigma limits to control charts. What are the
tail areas outside these limits?
3. Find the area under the bell curve included inside two sigma limits.
4. Find the percentage of area beyond six sigma limits. Express this in parts per
million.
5. A process peaks at 4. Its specification limits are 2 and 5. If the standard devia-
tion is 1, find the process capability indices C
p
and C
pk
.
References
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Events in Play, W. Pearson, London, 1718.
2. J. C. Friedrich Gauss. Available at http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss.
3. H. Fischer, A History of the Central Limit eorem: From Classical to Modern Probability
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4. Sir F. Galton, Natural Inheritance, MacMillan, 1889.
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Momentenproblem, MathematischeZeitschrift (in German), 8(3–4), 171–181, 1920.
6. L. Le Cam, e central limit theorem around 1935, Statistical Science, 1(1), 78–91,
1986.
7. D. J. Poirier, Intermediate Statistics and Econometrics: A Comparative Approach, MIT
Press, London, Cambridge, 1995.
8. Elvins, Volume Visualization. Available at http://www.cs.rug.nl/~michael/FANTOM
/FANTOM1a.pdf.
9. F. H. Hankins, Adolphe Quetelet as Statistician, Columbia University, New York, 1908.
10. P. F. Dahl, Flash of the Cathode Rays: A History of JJ omson’s Electron, CRC Press,
1997.
11. M. Norton, C. Bush, B. Atinaja and B. Steven, Electron Charge to Mass Ratio. Available
at http://www.siue.edu/~mnorton/Ratio.pdf.
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