Your local grocery store sells 1 lb. bags of potatoes. However, the 1 lb. bags do not weigh exactly 1 lb. If we let be the weight of a randomly selected 1 lb. bag of potatoes, historical data indicates that ~(1.02, 0.13). Local cash and carry store sells 5 lb. bags of potatoes, which also do not weigh precisely 5 lbs. If Y is the weight of a randomly selected 5 lb. bag, historical data indicates that ~(5.05, 0.15). If we randomly select five 1 lb. bags of potatoes and one 5 lb. bag of potatoes, what is the probability that the sum of the weights of the five 1 lb. bags exceeds the weight of one 5 lb. bag? (For this problem you can use R to get the probability, but you must show some work to convince us you know what you are doing to solve this problem.)