A random sample of 130 students is chosen from a population of 4,500 students. If the mean IQ in the sample is 120 with a standard deviation of 5, what is the 99% confidence interval for the students' mean IQ score?

Let x be number of T-Shirts made.

Therefore,
Revenues from the sell = 12*x = 12x
The cost making them = 20+(8*x) = 20+8x
Profits = 12x-(20+8x) = 12x -20-8x = 4x - 20

Now, this profit should be atleast $100. Then,
100<4x-20 => 100+20<4x => 120<4x => 120/4<x => x>30

Therefore, more than 30 T-shirts should be made in order to make atlease $100 profit.