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MAT 540 Chapter 14 Homework Problems

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The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week:
Time Between Emergency Calls (hr.)

Probability

1 .05 2 .10 3 .30 4 .30 5 .20 6 .05

1.00

Simulatetheemergencycallsfor3days(notethatthiswillrequirea“running,”or cumulative, hourly clock), using the random number table.
Computetheaveragetimebetweencallsandcomparethisvaluewiththeexpected value of the time between calls from the probability distribution. Why are the results different?
Howmanycallsweremadeduringthe3-dayperiod?Canyoulogicallyassumethatthisis an average number of calls per 3-day period? If not, how could you simulate to determine such an average?

The time between arrivals of cars at the Petroco Service Station is defined by the following proba- bility distribution:
Time Between Arrivals (min.)

Probability

1 .15 2 .30 3 .40 4 .15

1.00

Simulatethearrivalofcarsattheservicestationfor20arrivalsandcomputetheaverage time between arrivals.
Simulatethearrivalofcarsattheservicestationfor1hour,usingadifferentstreamof random numbers from those used in (a) and compute the average time between arrivals.
Comparetheresultsobtainedin(a)and(b).

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 follows:
0 .10 1 .10 2 .20 3 .25 4 .30 5 .05

1.00

Simulatethemachinebreakdownsperweekfor20weeks.
Compute the average number of machines that will break down per week.

Simulate the decision situation described in Problem 16(a) at the end of Chapter 12 for 20 weeks, and recommend the best decision.

Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution:
Repair Time (hr.)

Probability

1 .30 2 .50 3 .20

1.00

Simulate the repair time for 20 weeks and then compute the average weekly repair time.

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