Asian School of Business

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Asian School of Business PG Programme in
Management (2005-06) Course Quantitative
Methods in Management I Instructor Chandan
Mukherjee Session 10 Useful Theoretical
Distributions (contd.)
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Normal Distribution
X N (µ, s2)
- 8 lt x lt 8 - 8 lt µ lt 8 s gt 0
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Go to the Excel File normal-distn.xls and fit
the Normal Distribution. Do you feel that the
model describes the distribution satisfactorily?
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Exercise with Normal Distribution
What is the probability that the measurements are
within or 2mm?
Normal Distribution Properties
If X N (µ, s2) then (X- µ)/ s N(0,1)
gt Standard Normal Distribtuion
Standard Deviate
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Normal Distribution Properties
If X N (µ, s2) then P (µ - 2s lt X lt 2s)
? P (µ - 3s lt X lt 3s) ? P (µ - 6s lt X lt 6s)
? If your target measurement is 100 and the
tolerence limit is / 2 then what is the
tolerance limit for s in the system?
6
Six Sigma Quality Commonly defined as 3.4
defects per million opportunities . If you are
interested in learning about six sigma quality
standard, you may like to refer to the following
site http//www.isixsigma.com/library/content/si
x-sigma-newbie.asp
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Lognormal Distribution
X has a Lognormal Distribution with parameters µ
and s2, if loge(X) i.e. ln(X) has a Normal
Distribution with parameters µ and s2
E(X)
V(X)
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Example Fitting a Lognormal Distribution
Annual Sales (in Crores) of a product by a sample
of 50 firms
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Go to the Excel File lognormal-distn.xls and
fit the Lognormal Distribution. Do you feel that
the model describes the distribution
satisfactorily?
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Shares in Lognormal Distribution

• If X LN (µ, s2) then -
• Share of units below say, K
• P Y lt (lnK- µ)/ s)- s where Y N(0,1)
• What is the share in total sales of the firms
  with annual sales above 5 crores?
• What is the share of the top 5 of the firms?

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Measuring Concentration or Inequality in a
Distribution Lorenz Curve Lorenz Ratio (Gini
Co-efficient)
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Measuring Concentration or Inequality in a
Distribution Herfindahl Index