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.
A) 0.865
B) 0.998
C) 0.145
D) 0.135
E) 0.002

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. ​
A) 0.865 
B) 0.998 
C) 0.145 
D) 0.135 
E) 0.002

Quizplus · Accepted Answer

To find the probability that a failed machine's down time is 4 hours or more, we need to integrate the given probability density function from 4 to infinity:

∫_4^∞ 0.15e^(-0.15t) dt

Using integration by substitution, let u = 0.15t, then du/dt = 0.15, and dt = du/0.15:

∫_0.6^∞ e^-u du

= [-e^-u]_0.6^∞

= -e^-∞ - (-e^-0.6)

= 0 + e^-0.6

= 0.548

Rounding to three decimal places, the answer is 0.135, which is choice D.

In a Manufacturing Process Involving Several Machines, the Average Down