You’re trying to engineer a machine which produces cardboard boxes which are 10-inch cubes, each having a volume of 1000 cubic inches. Your production machine can’t quite do this, though; because some of the parts are loose, it builds boxes which are perfect cubes but the side-lengths L follow a uniform distribution L ∼ Unif(9, 11).(a) Find the distribution function for the volumes of the boxes.(b) Find the average value of the volume.(c) Boxes are rejected for being the wrong size if they have volumes above 1050 cubic inches or below 950 cubic inches. What percentage of the boxes made by this machine get rejected?(d) Find the variance of the volume.
