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January 11th, 2018, 09:08 AM   #1
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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:


However the right answer is 260-210/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,

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January 11th, 2018, 01:45 PM   #2
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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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