10. Specifications for the plastic material used in the action figure in problems 8 and 9 call for one of the ingredients to be between 5.94 percent and 6.06 percent, with a target composition of 6.00 percent. The current measuring and mixing procedures result in a normally distributed variation of this ingredient with a standard deviation of 0.030 percent. The properties of this plastic material are very inconsistent, and the toy company wants to begin reducing the variability of this troublesome ingredient. The company has decided to buy its supplies from fewer suppliers so there will be less variation in their compositions, maintain its equipment for more consistent operation, and train all employees to follow a standardized mixing procedure.

a. Before these improvements are put into place, what percentage of the plastic ma- terial will be out of specification if the process is centered correctly on target?

b. Once the improvements are made and the variation of the inconsistent ingredient is reduced so the standard deviation is 0.020 percent, how much reduction will this make in the percentage of out-of-specification material when the process is cor- rectly centered?