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A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 centimeters and standard deviation 0.1 centimeters. The specifications call for corks with diameters between 2.9 and 3.1 centimeters. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn’t fit in the bottle.) What proportion of corks produced by this machine is defective?
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