Question: 7.78 A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter for the corks produced is

7.78 A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter for the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm. The specifications call for corks with diameters between 2.9 and 3.1 cm. 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 are defective?

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