MAT540 Week3 Homework

MAT540 Week3 Homework

Chapter 14

1. The Hoylake Rescue Squad receives an emergency call every 1,2,3,4,5,or6 hours, according to the following probability distribution.The squad isonduty24 hours per day, 7 days per week:

Time Between Emergency Calls(hr.)

Probability

1 0.15

2 0.10

3 0.20

4 0.25

5 0.20

6 0.10

1.00

a. Simulate the emergency calls for 3days (notethatthiswillrequirea“running”,orcumulative,hourlyclock), usingtherandomnumbertable.

b. Computetheaveragetimebetweencallsandcomparethisvaluewiththeexpectedvalueofthetime between calls fromtheprobabilitydistribution.Whyare the resultdifferent?

2. ThetimebetweenarrivalsofcarsatthePetrocoServicesStationisdefinedbythefollowingprobabilitydistribution:

TimeBetweenEmergency Calls(hr.)

Probability

1 0.35

2 0.25

3 0.20

4 0.20

Simulatethearrivalofcarsattheservicestationfor20arrivalsandcomputetheaveragetimebetween arrivals.

a. Simulatethearrivalofcarsattheservicestationfor1hour,usingadifferentstreamofrandomnumbers fromthose used in(a)and compute the average time betweenarrivals.

b. Compare theresults obtained in(a) and(b).

3. TheDynacoManufacturingCompanyproducesaproductinaprocessconsistingofoperationsoffivemachines.Theprobabilitydistributionofthenumberofmachinesthatwillbreakdowninaweekfollows:

MachineBreakdownsPer Week

Probability

0 0.10

1 0.20

2 0.15

3 0.30

4 0.15

5 0.10

1.00

a. Simulatethe machine breakdowns per weekfor20 weeks.

b. Compute the average numberofmachinesthatwillbreakdown perweek.

4. Simulatethefollowingdecisionsituation for 20 weeks, andrecommend the bestdecision.

AconcessionsmanagerattheTechversusA&Mfootballgamemustdecidewhethertohavethevendors sellsun visors orumbrellas.Thereis a 30% chance of rain, a 15%chance ofovercastskies,anda55%chanceofsunshine,accordingtotheweatherforecastincollegejunction,wherethegameistobeheld.Themanagerestimatesthatthefollowingprofitswillresultfromeachdecision,given each setofweather conditions:Decision

5. Everytime amachine breaks down at the Dynaco ManufacturingCompany(Problem3), either1, 2,or 3 hoursarerequiredto fix it,accordingto the followingprobabilitydistribution:

Repair Time (hr.)

Probability

1

0.20

2

0.50

3

0.30

1.00