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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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?

Mathematics
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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..
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
so the entire range is 3.0 gallons per minute

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and 11.0-10.0 = 1.0 gallons per minute of that range
so there is a 1.0/3.0 = .33 probability that the rate is between 10.0 and 11.0
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
Let me know if that makes sense.
Oh wow, that completely makes sense. I was dividing 3/1 and getting 3. Your explanation helped a bunch. Thank you :)
no problem! good luck!

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