12. Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let mu denote the average alcohol contend for the population of all bottles of the brand under the study. Suppose that the sample mean is 8.2 grams with a standard deviation of 1.5 grams. n =50 x = 8.2 0 = 1.5 a. Find the 95% confidence interval for the mean alcohol content of the cough medicine. Report the margin of error and show all the work. b. Explain in words any non-statistics person can understand what the 95% confidence interval means. c. Would the 90% confidence interval be narrower or wider? Explain why. 13. What is meant by margin of error in a confidence interval