A machine is set to pump cleanser into a process at the rate of 8 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 7.5 to 9.5 gallons per minute. Find the variance of the
Distribution.
A)5.33
B)0.08
C)0.33
D)24.08

Question

Quizplus · Accepted Answer

The variance $ \sigma^2 $ of a uniform distribution defined over the interval [a, b] is given by the formula $ \sigma^2 = \frac{(b-a)^2}{12} $. Here, a = 7.5 and b = 9.5, so $ \sigma^2 = \frac{(9.5-7.5)^2}{12} = \frac{4}{12} = \frac{1}{3} = 0.33 $.

A Machine Is Set to Pump Cleanser into a Process