5.30 Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013

Question

5.30 Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality of a transformer, Exercise 2.53 (p. 54) Recall that two causes of poor power quality are "sags" and "swells". (A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer.) For Turkish transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. As in Exercise 2.53, assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. Also, assume that the number of sags and number of swells are both normally distributed. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week. a. What is the probability that the number of sags per week is less than 400? (0.9418 b. What is the probability that the number of swells per week is greater than 100? (I)

Explanation / Answer

the distribution is given to be normal distribution

the mean for sags = 353

standard deviation = 30

mean for swell = 184

standard deviation for sags = 25

we need to find the probability of sags being less then 400

the formula to be used = z = (x-mean)/standard deviation

now p(x<400) =

For x = 400, the z-value z = (400 - 353) / 30 = 1.56

Hence P(x < 400) = P(z < 1.56), now from the z table we will take the value of z score = 1.56

And that value will be the probability required.

= [area to the left of 1.56] = 0.9418

b) p(x>100) =

) For x = 100, z = (100 - 184) / 25 = -3.36

Hence P(x > 100) = P(z > -3.36) = [total area] - [area to the left of -3.36]

1 - [area to the left of -3.36]

now from the z table we will take the value of z score = -3.36

    = 1 - 0.0004 = 0.9996 =1

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