Question $112pts$ Let $x=$ the weight of a randomly selected adult American, and let us suppose that ${}_x=177$ lbs and ${}^{2}x=1024$ lbs$.$ A certain elevator can hold a maximum of $12$ adults. We want to figure out the mean and standard deviation of the potential loads the elevator would have to bear when it's at maximum occupancy. $($a$)$ If $x_1$ is the weight of the first person, $x_2$ is the weight of the second person, etc, write out an expression for $L$ where $L=$ load at maximum occupancy. We will assume that the weights of randomly selected persons are independent. $($b$)$ What is the mean of $L?$