Q1. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.27 inches. A sample of 9 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.23 and 30.32 inches long?
Q2. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.18 ounces. The weights of the sugar bags are normally distributed. What is the probability that 36 randomly selected packages will have average weight less than 15.955 ounces?