Suppose a product must go through an assembly line is made up 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. Define the flow time to be the total time it takes a product to go through the assembly line from start to finish.

a. What is the mean and standard deviation of the flow time? What is probability that the total time will be less than 920 seconds?
b. Now assume that the time required to complete each operation has a 0.40 correlation with the operation time immediately preceding it. What is the mean and standard deviation of the flow time? What is probability that the total time will be less than 920 seconds?
c. Now assume that the time required to complete each operation has a -0.40 correlation with the operation time immediately preceding it. What is the mean and standard deviation of the flow time? What is probability that the total time will be less than 920 seconds?
d. Explain the effects of positive and negative correlations on the previous results.