Question

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?

Answer 1

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..

Answer 2

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

Answer 3

so the entire range is 3.0 gallons per minute

Answer 4

and 11.0-10.0 = 1.0 gallons per minute of that range

Answer 5

so there is a 1.0/3.0 = .33 probability that the rate is between 10.0 and 11.0

Answer 6

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

Answer 7

Let me know if that makes sense.

Answer 8

Oh wow, that completely makes sense. I was dividing 3/1 and getting 3. Your explanation helped a bunch.

Thank you :)

Answer 9

no problem! good luck!