Suppose that a product must go through an assembly line that consists of five sequential operations. The time it takes to complete each operation is normally distributed with a mean of 180 seconds and standard deviation of 5 seconds. Let X denote the cycle time for the line, so that after X seconds each operation is supposed to be finished and ready to pass the product to the next operation in the assembly line.

a. If the cycle time X = 180 seconds, what is the probability that all five operations will be completed?

b. What cycle time will ensure that all operations are finished 98% of the time?