(The title is very clever, but you have to think about it.)*
This one is the last part of the last question of 2022 Specialist Mathematics Exam 2 (not online). It sparked a lot of discussion on the exam post, but seems worth its own WitCH. The question is clearly a mess, but what was intended, and how to think about the mess is not so clear, at least to us. (We showed the question to a professor of statistics, whose first reaction was “Ow!” We’ve applied the smelling salts, and we should be in possession of the professor’s second reaction soon.)
For clarification, we are (kinda sorta) told in the question stem that the masses of the empty cans are normally distributed, but we are told nothing else relevant, other than what’s given below.
Go for it (again).
*) Proving that the title is not really that clever.