Quality characteristic of filling teabags- The label weight on the package indicates that the mean is 5.5 grams of tea per bag. If the bags are under filled two problems arise. First, customer tea will no be as strong. Second, company could be in violation of the truth and lending law. If the mean amount exceeds the label weight the company is giving away product. Getting an exact amount is a problem because of the variations in temperatures ands humidity. About 170 bags per minute are filled. The following data (stored in the Teabags) are the weights, in grams, of a sample of 50 tea bags produced in one hour by one machine:

5.25 5.42 5.49 5.54 5.58
5.29 5.42 5.50 5.54 5.58
5.32 5.44 5.50 5.55 5.61
5.32 5.44 5.50 5.55 5.61
5.34 5.44 5.51 5.56 5.62
5.36 5.45 5.52 5.56 5.63
5.40 5.45 5.53 5.57 5.65
5.40 5.46 5.53 5.57 5.67
5.40 5.47 5.53 5.57 5.67
5.41 5.47 5.53 5.58 5.77

a. Construct a 99% confidence interval estimate for the population mean weight of the tea bags.
b. Is the company meeting the requirement set fourth on the label that the mean of tea in a bag is 5.5 grams?
c. Do you think the assumption needed to construct the confidence interval estimate in (a) is valid.