The Coca-Cola company conducted a market research and found that their loyal customers choose Coke Classic over Pepsi because they can clearly distinguish the difference in taste of the two products, and they like how Coke tastes better. In order to protect their trade secret, the manufacturing of Coca-Cola only labels the two most important flavorings of their Coke Classic as C1 and C2. To preserve the original taste that the customers like, the content of C1 in a 12 oz can must be between 32 to 34 mg, and C2 between 7 to 9 mg. Any can of Coke Classic with either one of the flavorings falling outside of this range would be considered defective (it could break a customers trust!). The flavoring process of the soda is a two-step serial process: 1) Add C1, and 2) Add C2.

The current process results in the content of C1 with a mean of 33 mg, and a standard deviation of 0.25 mg; the content of C2 has a mean of 8 mg and a standard deviation of 0.35 mg.

Coco-Cola noticed a recent fall in their sales and suspected that it may be due to an error-prone flavoring process. Their goal is to reduce the defect rate to be no more than 0.0013 (0.13%). They believe that reducing step 2)s standard deviation is the financially and logistically best way to go. The estimate cost is $100,000*x% to improve the standard deviation by x%. How much will it cost Coco-Cola to reach their goal?

Hint: P(not defective overall) = P(not defective in Step 1) * P(not defective in Step 2) . Use the information to find the target P(no defective in Step 2).