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normal distribution random number generation

• To: mathgroup at smc.vnet.net
• Subject: [mg51113] normal distribution random number generation
• From: cjkunkel at marauder.millersville.edu (Chris Kunkel)
• Date: Tue, 5 Oct 2004 04:36:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

Recently I have encountered a problem in Mathematica's normal
distribution random number generator.  The problem arises when I look
at the distribution of averages of a list of theses numbers.  That is,
I generate 1000 numbers and take their average.  I do this a number of
times and the plot a frequency distribution.  Consistently it seems to
be skewed positive.  Specifically, the number of occurrences less than
3 standard deviations is consistent with the expected number, but the
number greater than 3 is always larger (in some cases about twice the
expected number).

I was wondering if anyone else has noticed this and knows of a fix. 
Also, does anyone have code for a good quality normal distribution
random number generator?

Chris