In sci.stat.consult you write:

>Gordon Kenyon <[EMAIL PROTECTED]> wrote in sci.stat.edu:
>>In quantitative methods text-books for the social and behavioral
>>sciences one constantly sees the equation which describes the pdf for
>>both normal distributions in general and the standard normal
>>distribution.  I have never seen any basic warning that this
>>"description" of the standard normal distribution is only the density
>>function and not a computing formula of any kind.

>It's not? I'm pretty sure that in the past I have computed the
>population between two z scores by computing the definite integral
>with those z scores as limits. Granted, it's a lot more efficient to

Sorry, no dice.  It is impossible to analytically calculate a definite
intergral of any normal distribution function unless you use some method
from numerical analysis (See Feller).  You can analytically calculate the
indefinite integral of a normal distribution function but you have use a
polar coordinate transformation and calculate a double integral (See
Sheldon Ross, "A First Course in Probability" pp 200 for the proof.)

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