All you have to do is find the number of people such that the probability of the sample mean being above 1200/n is less than or equal to .001:
P(Z>(1200/n-76)/(12/sqrt(n)))=.499
and solve for n.
I think this is right, but sorry if it's not - i haven't actually done that tutorial (my class was on friday), and i haven't done any stats these holidays.