Question: The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.
(a) If the standard deviation remains at s = 0.02 inches, at what value should the supplier set the mean diameter of its large-cup lids so that only 1% are too small to fit? Show your method.
(b) If the mean diameter stays at m = 3.98 inches, what value of the standard deviation will result in only 1% of lids that are too small to fit? Show your method.
(c) Which of the two options in parts (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)