The weights of the population of cans of Coke are normally distributed with a mean of 12 oz and a population standard deviation of 0.12 oz. A sample of 9 cans is randomly selected from the population.
(a) Find the standard error of the sampling distribution. Round your answer to 4 decimal places.
(b) Using the answer from part (a), find the probability that a sample of 9 cans will have a sample mean amount of at least 12.05 oz. Round your answer to 4 decimal places.
(c) Using the answer from part (a), find the probability that a sample of 9 cans will have a sample mean weight between 11.97 oz and 12.04 oz. Round your answer to 4 decimal places.