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; and a transformer which has a random failure rate of one in every five years of operation.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 fail within 19 years?
A)0.1915
B)0.3085
C)0.383
D)0.5
E)0.6915

Question

Quizplus · Accepted Answer

We can use the normal distribution to approximate the probability of the transformer failing within 19 years.
First, we need to calculate the z-score:
z = (19 - 20) / 2 = -0.5
where 20 is the mean time to wear-out and 2 is the standard deviation.
Next, we need to find the probability of a z-score less than or equal to -0.5:
P(z ≤ -0.5) = 0.3085 (from standard normal distribution table)
So the answer is B, 0.3085.

The Plant Manager for the Local Electric Utility Company Wants