2. A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is .500 in. A bearing is acceptable if its diameter is within .003 of this target value. Suppose that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean equal to .501 and standard deviation equal to .002.
a) What percentage of the bearings produced will be acceptable ?
b) If three bearings are independently selected, what is the probability that at least one will be not acceptable ?