Respuesta :
Answer:
[tex] X \sim Unif(a=284.7, b = 310.6)[/tex]
And the density function is given by:
[tex] f(x) = \frac{1}{b-a}= \frac{1}{310.6-284.7}= 0.0386, 284.7 \leq x \leq 310.6[/tex]
And the cumulative distribution function is given by:
[tex] F(X) = \frac{x-a}{b-a}= \frac{x-284.7}{25.9}[/tex]
And we want the following probability:
[tex] P(X>300)[/tex]
And we can use the complement rule and we got:
[tex]P(X>300)= 1-P(X<300) = 1-F(300) = 1-\frac{300-284.7}{25.9}= 1-0.5907= 0.4093[/tex]
Step-by-step explanation:
Let X the random variable that represent the driving distance and we know that the distribution for X is given by:
[tex] X \sim Unif(a=284.7, b = 310.6)[/tex]
And the density function is given by:
[tex] f(x) = \frac{1}{b-a}= \frac{1}{310.6-284.7}= 0.0386, 284.7 \leq x \leq 310.6[/tex]
And the cumulative distribution function is given by:
[tex] F(X) = \frac{x-a}{b-a}= \frac{x-284.7}{25.9}[/tex]
And we want the following probability:
[tex] P(X>300)[/tex]
And we can use the complement rule and we got:
[tex]P(X>300)= 1-P(X<300) = 1-F(300) = 1-\frac{300-284.7}{25.9}= 1-0.5907= 0.4093[/tex]
And that would be the final answer for this case.
