A machine that produces ball bearings

Chapter 0, Problem 7.78

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A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the distribution of the diameters produced is well approximated by a normal distribution with mean 0.499 in. and standard deviation 0.002 in. What percentage of the bearings produced will not be acceptable?

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