With a capacity of 6,300 people, Royal Caribbean's Oasis of the Seas is the world's largest cruise ship. The average beer consumption over 15 randomly selected seven-day cruises on the ship was 81,740 bottles with a sample standard deviation of 4,590 bottles. Royal Caribbean would like to estimate the average beer consumption to plan its beer inventory levels on future cruises. (The ship certainly doesn't want to run out of beer in the middle of the ocean!)
a) Construct a 95% confidence interval to estimate the average beer consumption per cruise.
b) What assumptions need to be made about this population?