An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 175 brakes using Compound 1 yields an average brake life of 44,938 miles. A sample of 132 brakes using Compound 2 yields an average brake life of 45,825 miles. Assume that the population standard deviation for Compound 1 is 3642 miles, while the population standard deviation for Compound 2 is 2932 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

*ANSWER*: 735.773564