Suppose that a production manager needs to complete 5 tasks on a given day. All tasks' duration are Exponentially distributed with a mean of 1 hour, and they are statistically independent of each other. Tasks are sequentially executed, that is the manager carries out task 1 first, then after that task 2, etc.

1. Generate a snapshot realization (a single run) of the 5 tasks' duration, and calculate the total work time needed to complete the tasks. Does the time exceed 8 hours? If yes, by how much (that's the overtime)? [6 pts]

Instruction: Please clearly label each cell. Three points will be given for correctness and three points will be given for clarity of the implementation. Please answer the above questions in your Excel file.

2. "Running" your model 1000 times (that is simulate the problem 1000 times). What is the likelihood that overtime (more than 8 hours) would be needed? What is the expected overtime? Please provide the upper and lower limits of the 99% confidence interval of both estimates.

Instruction: Please clearly label each cell. Three points will be given for correctness and six points will be given for clarity of the implementation. Please answer the above questions in your Excel file.