Question

Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.

a.Would you consider 400 sags per week unusual, statistically? Explain.

b.Would you consider 100 swells per week unusual, statistically? Explain.

Short answer

(a) Not unusual

(b) Unusual

Step-by-step solution

Determining whether 400 sags per week is unusual or not

To check whether 400 sags per week is unusual or not, we will calculate the $$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{400-353}{30} \\ =\frac{47}{30} \\ =1.566 \end{gathered}$$

According to the z score value,400 sags per week is not unusual because z < 3.z-score values higher than 3 are unusual.

Interpreting whether 100 swells per week is unusual or not

To verify whether 100 swells per week is unusual or not, we will calculate the $$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{100-184}{25} \\ =\frac{-84}{25} \\ =-3.36 \end{gathered}$$

Based on the z score value,100 swells per week is unusualbecause it lies outside the standard deviation range where most of the observations lie.