A shipment of 10,000 cartons of fruit arrives at a distribution center with a nominal weight of 10 lbs per carton. A sample of 5 cartons is selected and weighed. The average weight of the sample is 10.2 lbs, and the standard deviation of weight among cartons is 2 lbs. Find a 95% confidence interval for the mean weight of all the cartons of fruit in the shipment.
