Let X and Y equal the respective numbers of hours a randomly selected child watches movies or cartoons on TV during a certain month. From experience, it is known that E(X) = 30, E(Y) = 50, Var(X) = 52, Var(Y) = 64, and Cov(X, Y)= 14. Twenty-five children are selected at random. Let Z equal the total number of hours these 25 children watch TV movies or cartoons in the next month. Approximate P(1970

Question

Let  X  and  Y  equal  the  respective  numbers  of  hours  a  randomly  selected child watches movies or cartoons on TV during a certain month. From experience, it is known that E(X) = 30, E(Y) = 50, Var(X) = 52, Var(Y) = 64, and  Cov(X, Y)= 14. Twenty-five children are selected at random. Let Z equal  the total number of hours these 25 children  watch  TV  movies or cartoons  in  the  next  month. Approximate P(1970 < Z < 2090)