In Pawnee, Indiana, the price of a pound of bacon, X, varies from day to day according to a normal distribution with mean of $4.12 and a standard deviation of $0.16. The price of a dozen eggs, Y , also varies from day to day according to a normal distribution with a mean of $1.94 and a standard deviation $0.06. Assume the prices of a pound of bacon and a dozen eggs are independent. (a) Find the probability that on a given day, the price of a pound of bacon is more than twice as expensive as a dozen eggs. That is, find P(X > 2Y ). (b) Ron Swanson needs to cook himself breakfast, so he buys 9 pounds of bacon and 7 dozen eggs. Find the probability that he paid more than $50.