Your consulting company has been hired by an airline to analyze data on passenger and luggage weights. The data refer to a 200 seat aircraft that is always full. You are given data that show that as a good approximation passenger weights W ~ N (150, 400) checked luggage weights B ~ N (60, 100) hand luggage weights H ~ N (10, 25) and that passenger weight, checked luggage weight, and hand luggage weight are mutually independent. All weights are in pounds.
a. The airline wants to know what maximum total weight limit on passengers plus luggage it should choose so that 95% of flights will be under the limit. (Total weight refers to the sum of weights of all passengers, plus all luggage.)
b. How would your answer change if, instead of being independent, W, B, and H have the following pairwise correlations: Corr(W, B) = .10 Corr(W, H) = 0 Corr(B, H) = .25