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lgbasallote

  • 2 years ago

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 between 6 to 9 km/L

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  1. amistre64
    • 2 years ago
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    12-5 = 7 |dw:1350993412929:dw|

  2. lgbasallote
    • 2 years ago
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    ahh finally...someone who understands

  3. amistre64
    • 2 years ago
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    iwould take a gander and say\[\frac{1}{7}{(9-6)}\]

  4. lgbasallote
    • 2 years ago
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    what's that 1/7 by the way?

  5. lgbasallote
    • 2 years ago
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    |dw:1350993820431:dw|

  6. amistre64
    • 2 years ago
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    a distribution curve has an area of 1 underneath it. since this is a uniform distribution. the "curve" is just a rectangle box with an area of 1 since the width is 7 units wide; the height of the box would have to be 1/7 to get an area of 1

  7. lgbasallote
    • 2 years ago
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    hmm...that's an intuitive way of solving it....and here i thought i have to do \[\huge \int \limits_a^b f(x)dx\]

  8. amistre64
    • 2 years ago
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    when it gets to normal distributions with a bell curve; they were nice enough to write down tables of for the integration :)

  9. lgbasallote
    • 2 years ago
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    ^?

  10. amistre64
    • 2 years ago
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    a z table is a table of probabilities; it is written up for the same reason that sin and cos tables are written up. So that we dont have to suffer thru the integration of some ungodly looking integral

  11. lgbasallote
    • 2 years ago
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    ...you have succeeded in confusing and scaring me at the same time....

  12. amistre64
    • 2 years ago
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    yay!! happy halloween :)

  13. lgbasallote
    • 2 years ago
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    it's already christmas from where i am

  14. amistre64
    • 2 years ago
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    hmmm, happy hanakah? ;)

  15. lgbasallote
    • 2 years ago
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    anyway...this would just be \[\int \limits_a^b \frac 1{b-a} dx\] yes?

  16. lgbasallote
    • 2 years ago
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    wait...that's wrong

  17. lgbasallote
    • 2 years ago
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    \[\int \limits_a^x \frac 1{b-a}dx\] yes?

  18. amistre64
    • 2 years ago
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    if you wanted to do the \[\int f(x)dx\]then a uniform distribution is a constant function \[\int_{5}^{12}k~dx=1\] \[12k-5k=1\] \[7k=1\] \[k=\frac17\] therefore \[\int_{6}^{9}\frac17~dx\]

  19. lgbasallote
    • 2 years ago
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    so...i am right...yes?

  20. amistre64
    • 2 years ago
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    1/(b-a) does generalize it yes. but the interval [a,x] seems a little off. that should simply be the interval across which you are integrating and should prolly not be confused with the other parts

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