Question

Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. 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. The power quality of transformers built in Turkey was investigated in Electrical Engineering (Vol. 95, 2013). 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. 1.57

b. Find the z-score for the number of swells for this transformer. Interpret this value. -3.36

Answer 1

Answer:

a

 $z-score = 1.57$

b

 $z-score_s = -3.36$

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  103  

    The  sample mean of  sag is  $\= x_1 = 353$

     The sample mean of swells is  $\= x_2 = 184$

    The standard deviation of  sag is  $s_1 = 30$

     The standard deviation of swells is  $s_2 = 25$

     The number of swell for a randomly selected transformer is  k  =  100

      The number of sag for a randomly selected transformer is  c  =  400

Generally the z-score for the number of swells is mathematically represented as

     $z-score_s = \frac{ k - \= x_2}{s_2}$

=>   $z-score_s = \frac{ 100- 184}{25}$

=>     $z-score_s = -3.36$

       

Generally the z-score for the number of sags is mathematically represented as    

      $z-score = \frac{ c - \= x_1}{s_1}$

     $z-score = \frac{ 400 - 353}{30}$

     $z-score = 1.57$