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?

And we can use the cumulative distribution function given by:

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

And then the final answer for this case would be

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:

And for this case the density function is given by:

And we want to calculate the following probability:

And we can use the cumulative distribution function given by:

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

And then the final answer for this case would be

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step-by-step explanation: