In a random sample of six ​people, the mean driving distance to work was 25.3 miles and the standard deviation was 4.7 miles. Assuming the population is normally distributed and using the​ t-distribution, a 99​% confidence interval for the population mean μ is (17.6, 33.0) ​(and the margin of error is 7.7​). Through​ research, it has been found that the population standard deviation of driving distances to work is 5.6. Using the standard normal distribution with the appropriate calculations for a standard deviation that is​ known, find the margin of error and construct a 99​% confidence interval for the population mean μ. Interpret and compare the results.