Suppose that the stock price for Burger Queen, $X per share, and the stock price for Dairy King, $Y per share, vary from day to day randomly according to a bivariate normal distribution with parameters H x = 67, Ox= 10, 4y= 38, Oy=4, p=0.8.

a) What is the probability that on a given day the price of stock for Burger Queen exceeds $75? That is, find P(X>75).

b) Suppose that on a given day the price of stock for Dairy King is $39. What is the probability that the price of stock for Burger Queen exceeds $75? That is, find P(X>75 Y = 39).

c) What is the probability that on a given day the price of stock for Dairy King is below $39? That is, find P(Y<39).

d) Suppose that on a given day the price of stock for Burger Queen is $75. What is the probability that the price of stock for Dairy King is below $39? That is, find P(Y<39 X = 75).

e) What is the probability that I share of Burger Queen stock is worth more than 2 shares of Dairy King stock? That is, find P(X> 2Y).

f) Alex bought 5 shares of Burger Queen stock and 8 shares of Dairy King stock. What is the probability that on a given day the value of his portfolio exceeds $600? That is, find P(5X + 8 Y> 600).