Suppose that the distribution of the weight of a

QUESTION:

Suppose that the distribution of the weight of a prepackaged “1-pound bag” of carrots is \(N(1.18, 0.07^2)\) and the distribution of the weight of a prepackaged “3-pound bag” of carrots is \(N(3.22, 0.09^2)\). Selecting bags at random, find the probability that the sum of three 1-pound bags exceeds the weight of one 3-pound bag. Hint: First determine the distribution of Y, the sum of the three, and then compute P(Y > W), where W is the weight of the 3-pound bag.