Suppose a certain mechanical component produced by a company has a width that is normally distributed with a mean μ = 2600 and a standard deviation σ = 0.6.
(a) What proportion of the components have a width outside the range 2599 to 2601?
(b) If the company needs to be able to guarantee to its purchaser that no more than 1 in 1000 of the components have a width outside the range 2599 to 2601, by how much does the value of a need to be reduced?