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Your organization purchases bottles of a popular commercial solvent for resale.  Each bottle is labeled as containing 32 fluid ounces of the solvent.  Your contract specifies that each bottle must contain 32 ± .125 ounces of the specified solvent.  Recently, you have noticed that some bottles appear to be out of specification.  Obviously, the most significant problem is bottles do not contain at least 31.875 ounces of solvent.  The results of a study of the bottle-filling process indicate an average of 31.995 ounces of solvent in each bottle with a standard deviation of approximately .075 ounces.  Based on this information, what proportion of filled bottles are out of specification?

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