A time-and-motion study measures the time required for an assembly line worker to perform a repetitive task. The data show that the time X required to bring a part from a bin to its position on an automobile chassis follows a Normal distribution with mean 11 seconds and standard deviation 2 seconds. The time Y required to attach the part to the chassis follows a Normal distribution with mean 20 seconds and standard deviation 4 seconds. The study finds that the times required for the two steps are independent.

a. Describe the distribution of the total time required for the entire operation of positioning and attaching a randomly selected part.

b. Management’s goal is for the entire process to take less than 30 seconds. Find the probability that this goal will be met for a randomly selected part.