Problem 1) A salesman is attempting to convince a factory manager to buy a new bottle-filling machine. He claims that it can dispense the fluid more accurately that the old machine, resulting in less waste. The objective is to fill bottles with at least 500 mL. but with as little extra fluid as possible. Assume a confidence level of 99%. a) The factory manager tests the new machine by filling 12 bottles. He measures the volume of each test bottle and calculates that the average test bottle contains 505 mL, with a sample deviation of 13 mL. What is the uncertainty in the measured volume? b) The factory manager insists that the salesman prove that the new machine can fill bottles to an average volume of 505 mL + 2 mL with 99% confidence. What would you recommend that the salesman do? State any assumptions you make. c) The old machine is known to fill bottles with an average volume of 510 mL and standard deviation of 4.2 mL. What percentage of the bottles are filled with less than 500 mL