Each morning the Roach Coach Express departs on its delivery rounds bringing nee

Question

Each morning the Roach Coach Express departs on its 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 gallon, and that fuel consumption is normally distributed. Using the Normal Distribution, if the total trip mileage for that day is 200 miles, what is the minimum amount of fuel (gallons) that the driver should start the trip with to ensure there is only a five percent chance of running out of fuel prior to completing the trip. Define the Random Variable.

Explanation / Answer

Lets say 'n' number of gallons is put Hence the mean number of miles that can be traveled with that much fuel in the tank... Mean = 15*n And Standard deviation = 3*sqrt(n) Now P[(15*n-200)/(3*sqrt(n))] = 0.05 i.e. (15*n-200)/(3*sqrt(n)) = -1.645 (value got from normal distribution table) Now solving the quadratic we get 2 roots....(check if correct) n = 12.2 or n = 14.6 Hence he should put either 12.2 gallons or 14.6 gallons so that there is only 5% chance of running out of fuel....

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