The desired target quality characteristic of a product of Hanson Component Manufacturing is 0.80. The customer-service manager knows that customers are likely to complain when the specification is off the desired quality characteristic by more than 0.025. On average, it costs the firm $2,600 to handle and resolve each complaint. The production manager of the Hanson Manufacturing suggests that the company test the product more thoroughly before shipping. The cost of additional testing and adjustments is estimated at $31.50 per unit.

Given the company's cost coefficient,k, what should the tolerance be (to five decimal places) before conducting additional testing and adjusting at the factory?(Do not round intermediate calculations and round final answer to 5 decimals places.)