A company makes a chemical product, and based on extensive experience they believe the critical-to-quality variable for this product has mean 410 and standard deviation 10.
(a) Suppose the process output is Normally distributed, and the lower/upper speci cation limits on this variable are LSL = 400; USL = 480. What proportion of manufactured products will not conform to speci cations?
(b) If the standard deviation remains constant, where should the process operators change the mean of the process to minimize the proportion of products that do not conform to speci cations?