capital goodes question

Question 4A.2 of CT 7 (2011 edition) asks:

Which of the following are capital goods:

(i) a newly built factory
(ii)a school,
etc.


The answer says (ii) is true, that a school is a capital good

The definition says:
"Capital - All inputs into production that have themselves been produced (e.g. factories, machines and tools)."

Can somebody explain me why "a school" is a capital good? In my view, it does not enter into production.


Many thanks

 

"Production" covers services too, so a school is included as capital since it produces education.