According to a Google search, the average height of male soccer players in the U.S. is normally distributed with mean 1.79 m with a standard deviation of 0.04 m. (a) For a randomly selected soccer team of 11 players, what is the probability that the average height of the players is less than 1.77 m? Calculate the probability by hand or in Minitab. (b) In view of the small sample size, must you make any additional assumptions to justify the answer to part (a)? Please provide a short explanation. (c) Set up the hypothesis test to test the true average height of male U.S. soccer players. Ho: versus H: (d) Determine the z statistic and p-value for the hypothesis test in part (c).