1) Suppose we have a randomly selected sample of 25 sheets from a batch with a normal distribution, an average of 30.0 inches, and a standard deviation of 0.60 inches. What is the probability that the average sample length falls between 30.03 and 30.30 inches?
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 $150. Construct a 99 percent confidence interval around the mean annual expenditure in the bar. (You have to show your work or intermediate steps to get full points) inches?
3) The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments for 1000 orders. The planner randomly selected 1000 orders and found that 200 orders were shipped late. Construct the 99% confidence interval for the proportion of orders shipped late. ( You have to show your work or intermediate steps to get full points)