lgbasallote
  • lgbasallote
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
Probability
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
12-5 = 7 |dw:1350993412929:dw|
lgbasallote
  • lgbasallote
ahh finally...someone who understands
amistre64
  • amistre64
iwould take a gander and say\[\frac{1}{7}{(9-6)}\]

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lgbasallote
  • lgbasallote
what's that 1/7 by the way?
lgbasallote
  • lgbasallote
|dw:1350993820431:dw|
amistre64
  • amistre64
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
lgbasallote
  • lgbasallote
hmm...that's an intuitive way of solving it....and here i thought i have to do \[\huge \int \limits_a^b f(x)dx\]
amistre64
  • amistre64
when it gets to normal distributions with a bell curve; they were nice enough to write down tables of for the integration :)
lgbasallote
  • lgbasallote
^?
amistre64
  • amistre64
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
lgbasallote
  • lgbasallote
...you have succeeded in confusing and scaring me at the same time....
amistre64
  • amistre64
yay!! happy halloween :)
lgbasallote
  • lgbasallote
it's already christmas from where i am
amistre64
  • amistre64
hmmm, happy hanakah? ;)
lgbasallote
  • lgbasallote
anyway...this would just be \[\int \limits_a^b \frac 1{b-a} dx\] yes?
lgbasallote
  • lgbasallote
wait...that's wrong
lgbasallote
  • lgbasallote
\[\int \limits_a^x \frac 1{b-a}dx\] yes?
amistre64
  • amistre64
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 \[\int_{6}^{9}\frac17~dx\]
lgbasallote
  • lgbasallote
so...i am right...yes?
amistre64
  • amistre64
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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