Suppose the weights of bags of potato chips coming from a factory follow a normal distribution with a mean of 12.8 ounces and a standard deviation of 0.6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviation so that only 1% of the bags weigh less than 12 ounces, then how small does the manager need to make the standard deviation? Show work.

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