# MAT 540 Week 3 Homework

Aug 7th, 2016
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Chapter 14 - 5 Questions - All Answered 1. 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: a. Simulate the emergency calls for 3 days (note that this will require a “running” , or cumulative, hourly clock), using the random number table. b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the result different? 2. The time between arrivals of cars at the Petroco Services Station is defined by the following probability distribution: 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 a different stream of random numbers from those used in (a) and compute the average..........

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Hoylake Rescue SquadProbability of Time between callsP(x)0.150.10.20.250.20.11Cumulative(lowerTimebound)between calls010.1520.2530.4540.750.96EV =3.55Average Time =0.48295356SimulationsimulationNumber1234567891011121314151617181920RN0.7247380.2345740.606020.5682410.0706030.75840.8620230.842610.3332750.9816340.0716490.1501650.3251080.0215380.9746940.4382230.3860.565150.2614730.555508Timebetweencalls52441555361231633434Cumulativeclock57111516212631344041434647535659636670Petroco serviceSimulationProbability0.350.250.20.2Cumulative00.350.60.81a. Avg Arrival timeb. Avg. arrival timeCompare a. and b.2.252.05Timebetweenarrival (min)1234Counts1234567891011121314151617181920RN0.6725789490.857076480.5207976950.2054258980.8658734450.874429310.4333172130.9439576040.8089046670.4474765990.2074982320.0709582250.2471577250.6741915980.1396017040.3337960140.0698998690.9612601260.2156707080.015616425Time between calls34214424421113111411RN0.3886683210.7720763450.468624960.3103420210.0453064580.938735930.2773976580.5348590950.6812197230.0821069390.2372851020.0923037710.2497896270.6327698870.9084686270.0361489350.1256337290.9329822510.7051340820.526489140.1683828710.464374780.7130234330.6071960470.5283131290.8923828670.2925276650.55675659Tim

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