Question

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of transformer voltage sags and swells, Exercise 2.76 (p. 86). Recall that for a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184.

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. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.a. Find the z-score for the number of sags for this transformer. Interpret this value.b. Find the z-score for the number of swells for this transformer. Interpret this value.​

Answer 1

a. z-score for the number of sags for this transformer is ≈ 1.57 . The number of sags found in this transformer is within the highest 6% of the number of sags found in the transformers.

b. z-score for the number of swells for this transformer is ≈ -3.36. The number of swells found in the transformer is extremely low and within the lowest 1%

Explanation:

z score of sags and swells of a randomly selected transformer can be calculated using the equation

z=
`(X-M)/(s)` where

• X is the number of sags/swells found

• M is the mean number of sags/swells

• s is the standard deviation

z-score for the number of sags for this transformer is:

z=
`(400-353)/(30)` ≈ 1.57

the number of sags found in the transformer is within the highest 6% of the number of sags found in the transformers.

z-score for the number of swells for this transformer is:

z=
`(100-184)/(25)` ≈ -3.36

the number of swells found in the transformer is extremely low and within the lowest 1%