This is a real question from a test, but I can not determine an approach to figure out the solution.

Can you guys use your head?

A student  cuts a four-foot long graphite rod with a two inch

diameter into two pieces with an infinitesimally narrow cut made at random

along the length of the rod. On the average, what would be the length of the shorter of

the two resulting pieces? Express your answer to two decimals.