Suppose that a cupcake must go through 3 stages before it is finally completed. First, it must be baked, which is normally distributed between 18 and 22 minutes. Then, it must be frosted, where the time is normally distributed with mean 8 minutes and standard deviation 3 minutes. Lastly, it must be boxed up. If the frosting time is less than 5 minutes, it only takes 2 minutes to box up. If the frosting time is between 2 and 6 minutes, it takes 3 minutes to box up. If the frosting time is more than 6 minutes, it takes 4 minutes to box up. Run 1,000 simulation for the total processing times for cupcakes.

1. What is the average processing time? 2. What is the maximum time? 3. What is the minimum time? 4. What's the probability it takes longer than 32 minutes to eat a cupcake?

Please utilize excel programing and show work for each question.