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anonymous

  • 5 years ago

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.5 to 12.5 gallons per minute. Find the probability that between 10.0 gallons and 11.0 gallons are pumped during a randomly selected minute. The answer is 0.33, how do I arrive at this answer?

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  1. sandra
    • 5 years ago
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    Right so if it's a uniform distribution, that means it's equally likely to be 9.5 as 9.6 as 10 as 12.5 etc..

  2. sandra
    • 5 years ago
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    so given that it's an equal probability to be any of the rates between 9.5 and 12.5, you want to know how much of that range 10.0-11.0 covers

  3. sandra
    • 5 years ago
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    so the entire range is 3.0 gallons per minute

  4. sandra
    • 5 years ago
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    and 11.0-10.0 = 1.0 gallons per minute of that range

  5. sandra
    • 5 years ago
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    so there is a 1.0/3.0 = .33 probability that the rate is between 10.0 and 11.0

  6. sandra
    • 5 years ago
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    fun fact is - since it's a uniform distribution, there is also a .33 probability that the actual rate falls between 9.5 and 10.5, 9.6 and 10.6 etc.. - basically any 1.0 gallon range covers 33% of the total distribution

  7. sandra
    • 5 years ago
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    Let me know if that makes sense.

  8. anonymous
    • 5 years ago
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    Oh wow, that completely makes sense. I was dividing 3/1 and getting 3. Your explanation helped a bunch. Thank you :)

  9. sandra
    • 5 years ago
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    no problem! good luck!

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