Suppose bearing company manufactures bearings of .5 inch diameter, but the true diameter is a normally distributed random variable with mean of .5"
a) If the standard deviation of diameter is .002, what percentage of the bearings meet the specifications of being between .497" and .503'?
b) How small does the standard deviation of the diameter need to be in order to ensure that 99 percent of the bearings meet the specification of being between .497" and .503'?