Aman who moves to a new city sees that there are two routes he could take to work. a neighbor who has lived there a long time he tells him route a will average 5 minutes faster than route b. the man decides to experiment. each day he flips a coin to determine which way to go, driving each route 10 days. he finds that route a takes an average of 49 minutes, with standard deviation 2 minutes, and route b takes an average of 50 minutes, with standard deviation 4 minutes. histograms of travel times for the routes are roughly symmetric and show no outliers. (alpha =0.05)

find a 95% confidence interval for the difference between the route b and route a commuting times. ( , )