Q111E Voltage sags and swells.聽Refer ... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 2: Q111E (page 111)

Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by鈥渟ags鈥� and 鈥渟wells鈥�) 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

Expert verified

(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 $z = \frac{V a l u e - M e a n}{S t a n d a r d d e v i a t i o n} = \frac{400 - 353}{30} = \frac{47}{30} = 1.566$

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 $z = \frac{V a l u e - M e a n}{S t a n d a r d d e v i a t i o n} = \frac{100 - 184}{25} = \frac{- 84}{25} = - 3.36$