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?

Answer 1

Answer:

$P(X$

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:

$P(X$

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:

$P(X$

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:

$P(X$

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