Question: 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 \[\overline{X}=\] 186 mg. The sample standard deviation was found to be s = 19.0 mg on this group. Assume that the population is normally distributed.

a. Find the margin of error for a 95% confidence interval. Round your answer to the nearest tenths. (2.5 points)

b. Find a 95% confidence interval for the mean m cholesterol content for all experimental eggs. Assume that the population is normally distributed. 2.5 points)