A random sample of 225 bolts from machine A contained 20 defective bolts, while an independently chosen, random sample of 400 bolts from machine B contained 32 defective bolts. Let p, be the proportion of the population of all bolts from machine A that are defective, and let p, be the proportion of the population of all bolts from machine B that are defective. Find a 95% confidence interval for P, -P, . Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) Lower limit: X Upper limit