Please show all formulas, please have this done by 7 am

points; ' Problem 6. (6 points) The number of users of an ATM machine has a Poisson Distribution with a mean of 3 per 10 minute interval. Find the standard deviation of the number of users in 30 minutes. Problem 7. (18 points) Consider random variables X and Y. We know that E(X) = 3 and EM = 5. Furthermore, Var(X) = 16 and Var(Y) = 25. X and Y are independent random variables. YOU MUST SHOW YOUR WORK AND EXPlAlN YOUR ANSWERS BELOW. 3.) Find Var(X3Y) (6 points) b.) Find E()(Y) + E(X)*E(Y) (6 points) c.) Find E(4X7Y) (6 points) Problem 8. (20 points) Assume that X is Normally distributed with a mean of 56 and a variance of 16. YOU MUST SHOW YOUR WORK USING A Z-CHART HERE. a. Find P(X > 53.5) (6 points) ' b. Find x0 such that P(X > X0) = .7 (7 points) c. Find x0 such that P(X