Fuel mileage is uniformly distributed between 5 km/L to 12 km/L. What is the probability that on the next trip, fuel mileage is 7.5 km/L?

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Fuel mileage is uniformly distributed between 5 km/L to 12 km/L. What is the probability that on the next trip, fuel mileage is 7.5 km/L?

Mathematics
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the probability distribution function is 1/(12-5) as seen from earlier question so for any mileage between 5 and 12, the probability will be 1/(12-5)
hmmm....
uniform probability distribution eh,

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^?
and i suppose that , measurements are in 0.l L, or are they in 0.5 L units?
what do you mean?
well if the millage was 7.45 does that get counted as 7.5 ?
Very bad question. Two things wrong with it. 1) The probability of anything on the "next" trip is quite dependent on the nature of the next trip. Will you be going east or west in Eastern Wyoming? It makes a very big difference! The expected value of gas mileage on a randomly selected trip would be a better question. 2) More importantly, it's a continuous distribution. The probability of a single value is ZERO (0).
i don't think so
@tkhunny i don't believe in bad questions....
but you post so many bad questions lgba
If it's a legitimate question p(7.5) = 0 for any CONTINUOUS distribution.
why so?
@UnkleRhaukus no question is bad to those who see clearly
but you havent provided enough information to answer this question, once again
that's what you think
there are actually enough information
so much so that tkhunny is right
what are the increments in milage ?
you look for too much information
hartnn was close. This distribution can be modelled as a rectangle. It's width is 7, the distance from 5 to 12. Thus, it's height must be 1/7. The probability that mileage will be between 5 and 6 can be read from the rectangle. It's a smaller rectangle of length 1 (6-5) and height 1/7. The probability that mileage will be greater than 8 can be read from the rectangle. It's a smaller rectangle of length 4 (12-8) and height 1/7. Do you see how this works?
hmm i don't see how that turns out to be 0 though
in real situation milage is a measured quantity, and it will come in incremental values
You didn't answer my question. Do you see how those two probabilities are calculated?
would it be because of the integral?
i did answer your question
You can talk integrals if you want, but a Uniform Distribution is easier. Geometry is sufficient. Given a single value, the width of the rectangle is zero (0). The height is still 1/7. The integral shoudl make it clear, though: \[\int\limits_{7.5}^{7.5} \frac{1}{7} dx = ?? \] Don't evaluate this integral. It is an eyeball problem. With the limits identical, it is zero (0).
geometry is boring though...
by the way...i thought \[\int \limits_a^a f(x)dx\] is 0 only when f(x) is even?
or was it for odd...
No. That makes no sense. Get that our of your head. It is zero. You are thinking of [-a,a] for odd functions. This is [a,a]. It's zero if it exsits at all.
oh...yeah....
i suck in calculus
if milage is measured in 0.5 Km/L increments then there are 14 possible out comes, and the probability of milage being 7.5 Km/L will be 1/14, if milage is measured in 0.1 Km/L then there are 70 possible out comes, and the probability of milage being 7.5 Km/L will be 1/70, as the increments \(\Delta x\) , get smaller and smaller , they approach \(\text dx\)
Time to stop sucking! More focus. Seems to me, after this brief exposure, that you are a little random about it. Just organize your thinking a little better.
@UnkleRhaukus there are no increments
If mileage is measured in 0.5 Km/L increments, you have written your own problem statement and not answered the question that is asked. I will grant, however, that this may have been additional information shared in class.
class? there's no class...
That does make it harder to discuss things in class, then, doesn't it?!
not class as in etiquette...
\[\frac1n\sum{\Delta x} \longrightarrow\frac 1n\int\text dx\]
...no increments.....
then you get zero, BUT you really should has specified that the increments are infinitesimals in the question if you wanted people to know what you ment
yes...
0...
yes . bad question
you just overcomplicate things
you assume data...bad answer
math maps reality , reality is complicated,
that's your opinion
then answer to your Hypothetical question is Useless , they answer to my variation on your question is not useless
You converted me, @UncleRhaukus. On an exam, I would answer this qeustion two ways. 1) Point out the obvious "definition" question that results int eh value zero (0), and 2) Quantize the distribution in some way, as you have done, clearly document me assumptions, and provide some sort of non-zero response. Of course, not everyone can do that on every question. If it was multip-choice and zero (0) wasn't on there, I would cry foul!

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