Answer to Question #216984 in Statistics and Probability for Sochen Oeng

Question

An assessment of the quality of the electrical power system in Turkey was the topic of an article published in Electrical Engineering​ (Mar. 2013). 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 380 kV was measured periodically​ (over 10-minute​ intervals). For transformers supplying heavy industry​ plants, the light flicker distribution was found to follow​ (approximately) a normal distribution with μ=2.2​% and σ=0.5​%. Suppose if the perception of light flicker exceeds 2.4​%, 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?

Answer 1

$P(X>2.4)=1-P(z<\frac{2.4-2.2}{0.5})$

$=1-P(z<0.4)$

$=1-0.6554$

$=0.3446$

Let 0.05 be the significance level. 0.3446 is greater than 0.05. Tha chance of electric flicker is 0.3446 which is high. Therefore, it is likely for a transformer supplying a heavy industry plant to be shut down due to light​ flicker.