1.) The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution: Time Between Arrivals (min.) Probability 1 0.25 2 0.3 3 4 0.35 0.1 a.) Simulate the arrival of cars at the service station for 20 arrivals and compute the average time between arrivals. b.) Simulate the arrival of cars at the service station for 1 hour, using different stream of random numbers from those used in (a) and compute the average time between arrivals. c.) Compare the results obtained in (a) and (b) to the expected value. 2.) The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week is as follows: Machine Breakdowns per week Probability 0 0.05 1 0.15 2 0.2 3 0.3 4 0.25 5 0.05 a.) Simulate the machine breakdowns per week for 20 weeks. b.) Compute the average number of machines that will break down per week and compare to the expected value. 3.) Simulate the following decision situation for 20 weeks and recommend the best decision. A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manage estimates that the following profits will result from each decision given each set of weather conditions: Decision Weather Rain Overcast Sunshine .30 .15 .55 Sun Visors Umbrellas $-500 2,000 $-200 0 $1,500 -900 4.) Every time a machine breaks down at the Dynaco Manufacturing Company (problem 2), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution: Repair Time (hr.) 1 2 3 Probability 0.25 0.55 0.20 a.) Simulate the repair time for 20 weeks b.) Compute the simulated average weekly repair time and compare to the expected value.