1. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.8 inches. A sample of 25 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.08 and 30.32 inches long?
2. A small town has a population of 20,000 people. Among these 1,000 regularly visit a popular local bar. A sample of 100 people who visit the bar is surveyed for their annual expenditures in the bar. It is found that on average each person who regularly visits the bar spends about $2400 per year in the bar with a standard deviation of $200. Construct a 99 percent confidence interval around the mean annual expenditure in the bar.