Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Twelve cows given bST produced an average of 25.0 kg/d of milk. Assume that the standard deviation of milk production is 2.10 kg/d.

1. Find a 95% confidence interval for the true mean milk production.
2. If the farms want the confidence interval to be no wider than 1.30 kg/d, what level of confidence would they need to use?
3. What sample size is necessary to estimate the true mean milk production within 1.5 kg/d with a 95% confidence?