In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places.

Question

In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function  . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places. ​

Quizplus · Accepted Answer

To find the probability that a failed machine's down time is 4 hours or more, we need to integrate the probability density function from t = 4 to t = infinity:

∫(t=4 to infinity) 0.1e^(-0.1t) dt

Using integration by substitution, let u = -0.1t, du/dt = -0.1, dt = du/-0.1:

= ∫(u=-0.4 to infinity) e^u (-0.1) du
= [-0.1e^u] from u=-0.4 to infinity
= (-0.1e^(-0.4))
= 0.135 (rounded to three decimal places)

Therefore, the probability that a failed machine's down time is 4 hours or more is 0.135, which corresponds to choice D.

In a Manufacturing Process Involving Several Machines, the Average Down