The Boston Marathon is the world’s oldest annual marathon, held every year since 1897. In 2011, 23,879 runners finished the race, with a mean time for all runners of 3:49:54 (about 230 minutes) with standard deviation 0:37:56 (about 38 minutes). Find the mean and standard deviation (in minutes) of the distribution of sample means if we take random samples of Boston marathon finishers of size:
(a) n = 10
(b) n = 100
(c) n = 1000