On a certain airline, the flight attendances collect trash during flights and deposit it all into a single receptacle. Airline management is thinking about instituting an on-board recycling program in which waste would be divided by the flight attendants and placed into three separate receptacles: one for paper, one for cans and bottles, and one for other trash.
The volume of each of the three types of waste on a given flight is normally distributed. The airline would maintain a sufficient amount of trash-receptacle space on each flight so that the probability that a given receptacle becomes full under the new system is the same as the probability that the single receptacle becomes full under the old system.
Would the new policy require the same amount of space, more space, or less space for trash storage on each flight? Explain your answer academically