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From: gknight@ut-ngp.UUCP (gknight)
Newsgroups: net.math.stat
Subject: Normal distribution probability problem.
Message-ID: <2792@ut-ngp.UUCP>
Date: Fri, 10-Jan-86 21:37:54 EST
Article-I.D.: ut-ngp.2792
Posted: Fri Jan 10 21:37:54 1986
Date-Received: Sun, 12-Jan-86 00:29:31 EST
Distribution: net
Organization: UTexas Computation Center, Austin, Texas
Lines: 21

Two questions from the same set of facts.  Assume you have two
populations, A and B, for which you have full information (i.e.,
the value of every event in each population).

	1)  If you draw a sample of size n = 1 from each population,
what is the probability that the sample from population A is larger
than the sample from population B?

	2)  Now assume the only information you have about the two
populations is based on samples of, say, size n = 10.  Thus you have
the mean and standard deviation of a sample from each population, but
know nothing about the individual events within the populations.  Now
what is the probability that a single sample drawn from population A
will be larger than one drawn from population B?

	I think the answer to (1) is simply a z-value and the
probability is the area under the normal curve.  But I haven't a clue
on how to work it out if you only have sample data.  I'm interested in
theory as well as an algorithm.  Any help will be appreciated.

			Thanks.