Respuesta :
Answer:
[tex] P(X<3.7)[/tex]
And we can use the cumulative distribution function given by:
[tex] F(x) = \frac{x-a}{b-a} , a \leq X \leq b[/tex]
And for this case we can write the probability like this:
[tex] P(X<3.7)= F(3.7) = \frac{3.7-3.5}{3.8-3.5} =0.667[/tex]
And then the final answer for this case would be [tex]\frac{2}{3}=0.667[/tex]
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:
[tex] X \sim Unif (a=3.5, b=3.8)[/tex]
And for this case the density function is given by:
[tex] f(x) = \frac{x}{b-a}= \frac{x}{3.8-3.5}=, 3.5 \leq X \leq 3.8[/tex]
And we want to calculate the following probability:
[tex] P(X<3.7)[/tex]
And we can use the cumulative distribution function given by:
[tex] F(x) = \frac{x-a}{b-a} , a \leq X \leq b[/tex]
And for this case we can write the probability like this:
[tex] P(X<3.7)= F(3.7) = \frac{3.7-3.5}{3.8-3.5} =0.667[/tex]
And then the final answer for this case would be [tex]\frac{2}{3}=0.667[/tex]
