Re: Finding a probability from a Mean and a Standard Deviation
You need one more piece of information, the distribution. For example, if you are told a Poker player makes $500 in an average session, with a standard deviation of $3,000 that could mean:
(1) Half the time she makes $3,500 and the other half she loses $2,500;
(2) One time in 37 she makes $18,500 and the other 36 times she breaks even;
(3) She has a Normal bell shape of outcomes centered at $500 with 1/3 between -$2,500 and $500, 1/3 between $500 and $3,500, 1/6 below -$2,500 and 1/6 above $3,500.
(4) Or an infinite number of other possibilities.
People often assume (3), which may not be a bad idea in some situations, especially for figuring probabilities between 25% and 75%. If it's an unusual situation or you need bigger or smaller probabilities, then all you can do is fall back on some general limits.
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