depends on a solar component, call it A farming operation has a solar powered wa
ID: 3074768 • Letter: D
Question
depends on a solar component, call it A farming operation has a solar powered water pump system that component A. To have the system work without interruption, the farm has another 24 solar components as back up so that if the current component fails, another component automatically takes over. Assume these components function independently of each other, and assume that each component have a mean life of 50 hours and standard deviation of 4 hours. After the pump is started, it will be inspected in 1300 hours. What is the probability that a pump will still be functioning at the end of the 1300-hour period? Should the farm consider inspecting the pump sooner?Explanation / Answer
Given: There are total 25 solar components.
Mean life of each component = 50 hours
Standard deviation of each component = 4 hours
Thus, variance = 4^2 = 16 hours
To solve this problem, we assume that the life of solar components follow a Normal distribution.
Since all the components are identical,
Total mean life for 25 components = 50 × 25 = 1250 hours
Total variance for 25 components = 25 × 16 = 400 hours
Thus, total standard deviation = 400 = 20 hours
Let X be the total life of pump.
Thus, to find P( X >= 1300)
For this, we first calculate the corresponding Z-value
Thus, Z = (1300 - 1250)/20 = 2.5
-> P(X >= 1300) = P(Z >= 2.5)
From Z-table, we get P(Z >= 2.5) = 0.0062
Thus, the required probability that the pump will still be functioning at the end of the 1300-hour period is 0.0062
Yes, the farm should consider inspecting the farm sooner as that will increase the probability of the pump to be still in a functioning condition.
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