An air-company estimates the following distributions for the weight of the passangers (attachment), where X is adult males, Y is adult females and B is children.

μ = 85kg and (sigma) = 10kg.

A plane is transporting 108 males, 72 woman and 66 children. What is the expected value and variance for the total weight of all the passangers, and which kind of distribution will it be?

I'm guessing it has something to do with the central limit theorem, and that it will be a normal distribution, but I'm not sure. Any help? Thanks!