The inspection division of the Putnam County Weights and Measures Department wants to estimate the actual amount of soft drink that is placed in 2-liter bottles at the local bottling plant of a well known soft-drink company. The bottling plant has told the division that the known standard deviation for 2-liter bottles is 0.05 liters. A) Find the margin of error from a sample of 80 bottles with 92% confidence interval for estimating the true population mean average.
B) Assume the random sample of eighty bottles obtained from this bottling plant indicates a sample average of 1.99 liters. Construct an 84% confidence interval for the true population average.
C) Suppose it is assumed that the true average was indeed 2.0 liters. Find the probability that a random sample of 40 bottles has a sample mean less than 2.01 liters ?
D) Suppose it is assumed that the true average was indeed 2.0 liters. Find the probability that a random sample of 33 bottles has a sample mean between 1.99 than 2.02 liters ?