Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of 3.10 per gallon and an upper bound of 3.70 per gallon. What is the probability a randomly chosen gas station charges more than 3.25 per gallon?

Answer :

Given :

The lower bound, $a = 3.10$

The upper bound, $b = 3.70$

Solution :

→ The probability that a randomly chosen gas station charges more than $3.25 per gallon :

$∴ P (x > 3.25) = \int_{3.25}^{3.7} f (x) d x$ $= \int_{3.25}^{3.7} \frac{1}{0.6} d x$ $= \frac{1}{0.6} {[x]}_{3.25}^{3.7}$ $= \frac{1}{0.6} [3.7 - 3.25]$ $= 0.75$

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