Chapter 5.5, Problem 7E

Suppose that the distribution of the weight of a prepackaged “1-pound bag” of carrots is $N\left(1.18,0.072\right)$ and the distribution of the weight of a prepackaged “3-pound bag” of carrots is $N\left(3.22,{0.09}^2\right)$.

Selecting bags at random, find the probability that the sum of three 1-pound bags exceeds the weight of one 3-pound hag. Hint First determine the distribution of Y, the sum of the three, and then compute $P\left(Y>W\right)$, where W is the weight of the 3-pound bag.