Question: A machine is set to pump cleanser into a process at the rate of 5 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 4.5 to 7.5 gallons per minute.

1. Find the probability that the machine pumps less than 8.75 gallons during a randomly selected minute.
2. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute
3. Would you expect the machine to pump more than 12.85 gallons per minute d) What is the average gallons per minute ?
   e) Find the variance of the distribution.
   f) What is the 50th percentile for this distribution?
   
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