statistics
posted by looking for someone to varify my work please .
An experimental egg farm is raising chickens to produce low cholesterol eggs. A lab tested 12 randomly selected eggs and found that the mean amount of cholesterol was x = 186 mg. The sample standard deviation was found to be s = 19.0 mg on this group. Assume that the population is normally distributed.
Question: Find the margin of error for a 95% confidence interval. Round your answer to the nearest tenths.
Answer: 1.96(19/√16) = 9.31
Question: Find a 95% confidence interval for the mean µ cholesterol content for all experimental eggs. Assume that the population is normally distributed.
Answer:
1.96 – 9.31 = 7.35
1.96 + 9.31 = 11.27

Why is it the "√16" when n  1 = 11?
Standard error of the mean = Standard deviation/√(n1)
95% confidence interval = mean ± 1.96 SE. Why are you not using mean = 186?