Problem 1: Soft drinks are put into bottles that hold a nominal 200 ml, but the filling machine introduces a standard deviation of 10 ml. These bottles are packed into cartons of 25 and exported to a market which insists that the mean weight of a carton is at least the quantity specified by the manufacturer. To make sure this happens, the bottler sets the machine to fill bottles to 205 ml. What is the probability that a carton chosen at random fails the quantity test? Problem 2: A machine produces parts that have a standard deviation in length of 1.4 cm. A random sample of 100 parts has a mean length of 80 cm. What is the 95% confidence interval for the mean length of all parts