A machine is set to pump cleanser into a process at the rate of 7 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 6.5 to 9.5 gallons per minute. Find the probability that between 7.0 gallons and 8.0 gallons are pumped during a randomly selected minute.
A) 1
B) 0.33
C) 0
D) 0.67

Question

Quizplus · Accepted Answer

The probability density function of the uniform distribution is constant over the interval, so the probability of any subinterval is the length of the subinterval divided by the length of the entire interval. In this case, the probability of pumping between 7.0 and 8.0 gallons is (8.0 - 7.0) / (9.5 - 6.5) = 0.33.

A Machine Is Set to Pump Cleanser into a Process