A shipping facility handles two types of cargo boxes: Premium, PPP, and Economy, EEE. The masses, in grams, of Premium boxes are distributed as P∼N(850,302)P \sim \text{N}(850, 30^2)P∼N(850,302) and Economy boxes are distributed as E∼N(600,252)E \sim \text{N}(600, 25^2)E∼N(600,252).
A Premium box and an Economy box are selected at random.
Find the probability that the mass of the Premium box is less than 140% of the mass of the Economy box.
Two Premium boxes are chosen at random.
Find the probability that their masses differ by more than 45 g.
The facility ships boxes on heavy-duty pallets. Each pallet contains either 6 Premium boxes or 8 Economy boxes. The mass of an empty pallet, WWW, is distributed as W∼N(2000,1002)W \sim \text{N}(2000, 100^2)W∼N(2000,1002).
Find the probability that a pallet of 8 Economy boxes has a greater total mass than a pallet of 6 Premium boxes.