Question

In a certain country, the weekly demand for gasoline is best modeled according to the triangular distribution between 50.45 million and 76.75 million gallons, with a peak (mode) of 63 million gallons. The government wants to know how many gallons of gasoline it should import each week so that shortages of gasoline occur no more than 3% of the time. How many gallons of gasoline should this country import each week?

a) 54.2 million gallons
b) 60.8 million gallons
c) 66.4 million gallons
d) 72.0 million gallons

Answer 1

To find out how many gallons of gasoline the country should import each week, we need to find the value at the 3% point in the triangular distribution. By using the formula for the triangular distribution, we can calculate that the country should import approximately 54.2 million gallons of gasoline each week.

Step-by-step explanation:

To determine how many gallons of gasoline this country should import each week, we need to find the value that corresponds to the 3% point in the triangular distribution.

Since the mode of the distribution is 63 million gallons, we can use the formula for the triangular distribution to find the value at the 3% point.

Using the formula:

x = a + (b - a) * (p - c)/(d - c)

We substitute a = 50.45 million gallons, b = 76.75 million gallons, c = 63 million gallons, d = 76.75 million gallons, and p = 3%.

By solving this equation, we find that x ≈ 54.2 million gallons.

Therefore, the country should import approximately 54.2 million gallons of gasoline each week.