The daily demand for gasoline in a metropolitan area is best modeled according to the Triangular distribution between 1.25 million and 2.05 million gallons, and with a peak (mode) of 1.85 million gallons. The city receives 1.95 million gallons of gasoline on daily basis; however possible shortages on a few days during the year may force the city council to use the city's strategic reserves. Approximately during how many days of the year is the city expected to experience gasoline shortages. Round your answer to the nearest whole number. For example, "1.4582 days" should be entered as: "1".
I have applied the CDF (Cumulative Distribution Function) of Triangular Distribution:
where:
a(Minimum amount) = 1.25 million gallons,
b(Maximum amount) = 2.05 million gallons,
c(Peak value) = 1.85 million gallons,
x(Given value) = 1.95 million gallons
As per my understanding, I have applied the following formula to get the solution:
CDF = 1- (((b-x)^2/((b-a) (c-a)))
Number of days of the year city expected to gasoline shortages = CDF * 365 = 7 (approximately).
But this answer is wrong.
Could you please let me know what is the best solution for this problem?
Issue regarding Triangular Distribution Function calculation
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