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 10.0 to 13.0 gallons per minute. Would you expect the
Machine to pump more than 12.85 gallons per minute?
A)Yes, since .95 is a high probability.
B)No, since .95 is a high probability.
C)Yes, since .05 is a high probability.
D)No, since .05 is a low probability.

Question

Quizplus · Accepted Answer

The uniform distribution means that every outcome in the interval 10.0 to 13.0 gallons per minute is equally likely. To find the probability of the machine pumping more than 12.85 gallons per minute, we calculate the proportion of the interval from 12.85 to 13.0, which is (13.0 - 12.85) / (13.0 - 10.0) = 0.15 / 3 = 0.05. This means there's a 5% chance of pumping more than 12.85 gallons per minute, which is considered low.

A Machine Is Set to Pump Cleanser into a Process