The length of an injected-molded plastic case that holds tape is normally distributed with a mean length of 90.2 millimeters and a standard deviation of 0.10 millimeters.

(a) What is the probability that a part is longer than 90.30 mm or shorter than 89.7 mm?

(b) What should the process mean be set at to obtain the greatest number of parts between 89.7 and 90.30 mm?

(c) If parts that are not between 89.7 and 90.30 mm are scrapped, what is the yield for the process mean that you selected in part (b)?

Round z-score to 2 d.p. and use Appendix A, Table I.