Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standard deviation of milk production is 2.25 kg/d and the distribution is normal. (a) Find a 99% confidence interval for the true mean milk production. (b) If the farms want the confidence interval to be no wider than 2.5 kg/d, how many cows should they include in the study