The following information refers to 11-13 The plant manager for the local electr
ID: 3304565 • Letter: T
Question
The following information refers to 11-13 The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation (Reliability = 0.5); and a transformer which has a random failure rate of one in every five years of operation (Reliability = 0.8). 11. If he were to add both a backup generator and a backup transformer, what would be the probability that this system would perform reliably for a period of one year? A) 0.48 B) 0.60 C) 0.72 D) 0.75 E) 0.96 12. If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years, what is the probability that it will wear out within 19 years? A) 0.1915 B) 0.3085 C) 0.383 D) 0.5 E) 0.6915 13. If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years, what service life should the manufacturer specify in order to have a .9332 probability that it will last at least that long before wearing out? A) 17 years B) 18 years C) 19 years D) 20 years E) 21 years
Explanation / Answer
11. Since the reliability of transformer is 0.8, the reliability of the system is always greater than 0.8. Hence,
Option E is correct.
12. P(X < 19)
= P(z < (19 - 20)/2)
= P(z < -0.5)
= 0.3085
Option B is correct.
13. z score related to 0.9332 probability = 1.50
Hence,
Service life = 20 - 1.5*2 = 17 years
Option A is correct.
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