a. A manufacturing company has developed a fuel-efficient machine that combines

Question

a. A manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is designed to deliver 7.0 gallons of cleaner per minute at 1,000 pounds per square inch of pressure washing. In fact, it delivers an amount at random anywhere between 5.5 and 8.5 gallons per minute. Assume that the RV X, the amount of cleaner delivered, is an uniform RV with probability density f(x) = 1/2 for 6.5 < x < 8.5. What is the probability that more than 7.3 gallons of cleaner are dispensed per minute?

Explanation / Answer

Here, we have to use the uniform distribution for finding the probability.

Here, we have to find P(X>7.3)

We are given a = 6.5 and b = 8.5

We have f(x) = ½ = 0.5 for a<X<b

P(X>7.3) = (b – x) / (b – a) = (8.5 – 7.3) / (8.5 – 6.5) = 1.2 / 2 = 0.6

Required probability = 0.6

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