Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50

Question

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges less than $3.70 per gallon?

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Amaya 4 months 2021-10-13T18:18:19+00:00 1 Answer 0 views 0

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    2021-10-13T18:19:37+00:00

    Answer:

     P(X<3.7)

    And we can use the cumulative distribution function given by:

     F(x) = \frac{x-a}{b-a} , a \leq X \leq b

    And for this case we can write the probability like this:

     P(X<3.7)= F(3.7) = \frac{3.7-3.5}{3.8-3.5} =0.667

    And then the final answer for this case would be \frac{2}{3}=0.667

    Step-by-step explanation:

    For this case we define our random variable X “price of gasoline for a city in the USA” and we know the distribution is given by:

     X \sim Unif (a=3.5, b=3.8)

    And for this case the density function is given by:

     f(x) = \frac{x}{b-a}= \frac{x}{3.8-3.5}=, 3.5 \leq X \leq 3.8

    And we want to calculate the following probability:

     P(X<3.7)

    And we can use the cumulative distribution function given by:

     F(x) = \frac{x-a}{b-a} , a \leq X \leq b

    And for this case we can write the probability like this:

     P(X<3.7)= F(3.7) = \frac{3.7-3.5}{3.8-3.5} =0.667

    And then the final answer for this case would be \frac{2}{3}=0.667

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