Refer to the previous exercise. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately
7.90. 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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Chapter 7 Solutions
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