Question

In an assessment of the quality of the electrical power​ system, one measure of quality is the degree to which voltage fluctuations cause light flicker in the system. The perception of light flicker x when the system is set at 380kV was measured periodically​ (over 10-minute​ intervals). For transformers supplying heavy industry​ plants, suppose the light flicker distribution was found to follow​ (approximately) a normal distribution with μ=2.8% and σ=0.6.

If the perception of light flicker exceeds 3.3%, the transformer is shut down and the system is reset. How likely is it for a transformer supplying a heavy industry plant to be shut down due to light​ flicker?

there is a ? probability that a transformer supplying a heavy industry plant will need to be shut down.

(round to three decimal places as needed)

Answer 1

The likelihood of a transformer supplying a heavy industry plant being shut down due to light flicker can be determined by finding the probability that the perception of light flicker exceeds a certain threshold. In this case, the threshold is set at 3.3%. We can use the normal distribution to calculate this probability.

Step-by-step explanation:

The likelihood of a transformer supplying a heavy industry plant being shut down due to light flicker can be determined by finding the probability that the perception of light flicker exceeds a certain threshold. In this case, the threshold is set at 3.3%.

Since the light flicker distribution follows a normal distribution with a mean (μ) of 2.8% and a standard deviation (σ) of 0.6, we can use the normal distribution to find the probability.

To find the probability, we need to calculate the area under the normal curve to the right of 3.3%. This represents the probability that the light flicker exceeds 3.3%.

Using a standard normal table or a calculator with normal distribution functions, we can find this probability. The result will give us the likelihood of a transformer being shut down due to light flicker.