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January 11th, 2018, 09:08 AM  #1 
Newbie Joined: Jan 2018 From: Sweden Posts: 1 Thanks: 0  Why use variance instead of standard deviation?
This drives me crazy, The question is simple: A manufacturing process has the expected value of 200minutes and standard deviation of 10minutes The reset process has the expected value of 30 minutes with the standard deviation 3 minutes Compute the probability that the sum of the manufacturing and reset time is no more than 260 minutes. Using the central limit theorem I thought it would be straight forward like usually: 260210/13 However the right answer is 260210/sqrt(100+9) To me this is not logic, can someone explain why I would want to take the square root of the combined variances when I already have the individual square roots given? Best regards, John 
January 11th, 2018, 01:45 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,524 Thanks: 588 
It comes from a theorem of elementary probability theory. The variance of the sum of independent random variables is the sum of the variances. Adding standard deviations gives you a wrong answer.


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central limit theorem, deviation, standard, variance 
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