Case Situaton: Beauty lotion is a skin-moisturizing product that contantains rich oils, blended especialy for overly dry or neglected skin. The product is sold in 5-once bottles by a wide range of retail outlets. In an on going review of product quality and consistency, the manufacturer of Beauty Lotion found a sample average product volume of 5.2 ounces per unit with a sample standard deviation of 0.12 ounces, when a sample of n=144 observations was studied.
Question 1: Calculate the range within which the population average volume can be found with 99 percent confidence.
Question 2: Assuming that s=0.12 cannot be reduced, and a sample size of n=144, what is the minimum range within which the sample average volume must be found to justify with 99 percent confidence the advertised volume of 5 ounces?