Each morning, the Roach Coach Express departs on it delivery rounds, bringing ne

Question

Each morning, the Roach Coach Express departs on it delivery rounds, bringing needed donuts, hot coffee and similar nourishment to corporate clients at various locations around Colorado Springs. Assume that the Roach Coach (a converted bus) averages 15 miles per gallon, with a standard deviation of 3 miles per galon, and that fuel consumption is Normally Distributed. Using tghe Normal Distribution, if the total trip mileage for that day is 2oo miles, what is the minimum abount of fuel (gallons) that the driver should start the trip with to ensure there is only a five percent chance of running ou of fuel prior to completing the trip. ((Define the Random Variable).

Explanation / Answer

The random variable is the averge miles traveled. In this case we look at 200 miles/15=13.33 gallons for the trip. Now we notice a standard deviation of 3 so we look at 15/203 and 15/197 15/203=13.53 15/197=13.133 In this case, we need to know with a 5% chance of running out of gas. We can tell this is the 15/203 for a total of 13.53 gallons since the standard deviation estimates on the high side

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