MAT540 Homework Week 3 Page 1 of 2 MAT540 Week 3 HomeworkChapter 14 1. The Hoylake Rescue Squad receives an emergency callevery 1 2 3 4 5 or 6 hours according to the followingprobability distribution. The squad is on duty 24 hours per day 7days per week: Time Between Emergency Calls (hr.) Probability 10.05 2 0.10 3 0.30 4 0.30 5 0.20 6 0.05 1.00 a. Simulate theemergency calls for 3 days (note that this will require arunning or cumulative hourly clock) using the random numbertable. b. Compute the average time between calls and compare thisvalue with the expected value of the time between calls from theprobability distribution. Why are the results different? 2. Thetime between arrivals of cars at the Petroco Service Station isdefined by the following probability distribution: Time BetweenArrivals (min.) Probability 1 0.25 2 0.30 3 0.35 4 0.10 1.00 a.Simulate the arrival of cars at the service station for 20 arrivalsand compute the average time between arrivals. b. Simulate thearrival of cars at the service station for 1 hour using adifferent stream of random numbers from those used in (a) andcompute the average time between arrivals. c. Compare the resultsobtained in (a) and (b). 3. The Dynaco Manufacturing Companyproduces a product in a process consisting of operations of fivemachines. The probability distribution of the number of machinesthat will break down in a week follows: MAT540 Homework Week 3 Page2 of 2 Machine Breakdowns per Week Probability 0 0.05 1 0.15 2 0.203 0.30 4 0.25 5 0.05 1.00 a. Simulate the machine breakdowns perweek for 20 weeks. b. Compute the average number of machines thatwill break down per week. 4. Simulate the following decisionsituation for 20 weeks and recommend the best decision. Aconcessions manager at the Tech versus A&M football game mustdecide whether to have the vendors sell sun visors or umbrellas.There is a 30% chance of rain a 15% chance of overcast skies anda 55% chance of sunshine according to the weather forecast inCollege Junction where the game is to be held. The managerestimates that the following profits will result from eachdecision given each set of weather conditions: Weather ConditionsDecision Rain Overcast Sunshine .30 .15 .55 Sun visors $-500 $-200$1500 Umbrellas 2000 0 -900 5. Every time a machine breaks downat the Dynaco Manufacturing Company (Problem 3) either 1 2 or 3hours are required to fix it according to the followingprobability distribution: Repair Time (hr.) Probability 1 0.25 20.55 3 0.20 1.00 a. Simulate the repair time for 20 weeks and thencompute the average weekly repair time.