The same qn was posted in yahoogroups, and here is what one of the posters replied. I m just doing cut n paste ..
lets first simplify it
lets say that there are 12 units of something, and 4 are gone every month.
4 will last 1 month
4 will last 2 month
4 will last 3 month
so the average age would be 2 (mean/median of 1,2,3).
if there were 16 units and 4 are gone every month, then the average age would
be mean/median of (1,2,3,4) = 2.5.
generalizing it: if there are n months when there are no units left.
ans would be: n/2 + 0.5
So for this problem , n is (150,000 / 3000) = 50. So each hair would last 50/2 + 0.5 = 25.5 months.