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6. A box with 1000 coins is shaken until they are all randomly heads up or tails up and the number of heads is counted.

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6. A box with 1000 coins is shaken until they are all randomly heads up or tails up and the number of heads is counted. If this trial is repeated many times, what is the root mean square average of the quantity (nw-nr) where nw is the number of heads and my is the number of tails? (Use the Gaussian approximation.)

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