A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 47 patients. The effective period of the tranquilizer for the 47 patients have an average of 2.455 hours and a standard deviation of 0.334 hours. Construct a 99% confidence interval for the population average length of time. Also find the margin of error.