Question

solve the problem.

a machine is set to pump cleanser into a process at the rate of 6 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 5.5 to 8.5 gallons per minute. what is the probability that at the time the machine is checked it is pumping more than 6.5 gallons per minute?

.25
.7692
.667
.50

Explanation:

Identify the distribution parameters

Using the Continuous Uniform Distribution knowledge point

$$
LATEXBLOCK0
$$

Define the probability density function

Using the Continuous Probability knowledge point

$$ f(x) = \frac{1}{b - a} = \frac{1}{8.5 - 5.5} = \frac{1}{3},\quad 5.5 \le x \le 8.5 $$

Calculate the target probability

Using the Continuous Probability knowledge point

$$
LATEXBLOCK1
$$

Answer:

• .25
• .7692
• .667 (Correct answer)
• .50