12.10. The following is an example of aid to a materials review board. In a plant manufacturing soap and cosmetics, a question arose as to whether to use a lot of caps for cologne bottles. Accordingly tests were made on the distribution of cap strength (the torque which would break the cap) and the distribution of the torque which the capping machine would apply to a cap. They found in inch-pounds, respectively, x-bar ¼ 11:1; sx ¼ 2:80; y-bar ¼ 8:0; sy ¼ 1:51 Assuming independence (very safe here) and normality, estimate the average and standard deviation of the margin of safety, w¼xy. Estimate the percentage of caps that can be expected to break by a negative w value.