Respuesta :
Answer:
a
[tex]z-score = 1.57[/tex]
b
[tex]z-score_s = -3.36[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 103
The sample mean of sag is [tex]\= x_1 = 353[/tex]
The sample mean of swells is [tex]\= x_2 = 184[/tex]
The standard deviation of sag is [tex]s_1 = 30[/tex]
The standard deviation of swells is [tex]s_2 = 25[/tex]
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
[tex]z-score_s = \frac{ k - \= x_2}{s_2}[/tex]
=> [tex]z-score_s = \frac{ 100- 184}{25}[/tex]
=> [tex]z-score_s = -3.36[/tex]
Generally the z-score for the number of sags is mathematically represented as
[tex]z-score = \frac{ c - \= x_1}{s_1}[/tex]
[tex]z-score = \frac{ 400 - 353}{30}[/tex]
[tex]z-score = 1.57[/tex]
The z-score for the number of sags for this transformer is 1.57.
And the z-score for the number of swells for this transformer is -3.36.
Given that,
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 that 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.
We have to find,
Find the z-score for the number of sags for this transformer.
Find the z-score for the number of swells for this transformer.
According to the question,
For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353,
the standard deviation of the sag distribution is 30 sags per week.
the transformers is randomly selected and found to have 400 sags.
Therefore,
The z-score for the number of sags for this transformer,
[tex]\rm Z_s_c_o_r_e = \dfrac{Randomely \ selected \ transformers \ of \ sags- Mean \ number \ of \ sags }{Standard \ deviation \ of \ sags}\\\\ Z_s_c_o_r_e= \dfrac{400-353}{30}\\\\ Z_s_c_o_r_e= \dfrac{47}{30}\\\\ Z_s_c_o_r_e= 1.57[/tex]
Sample of 103 transformers built for heavy industry, the mean number of sags per week was 184,
the standard deviation of the sag distribution is 25 sags per week.
the transformers is randomly selected and found to have 100 sags
Therefore,
The z-score for the number of sags for this transformer,
[tex]\rm Z_s_c_o_r_e = \dfrac{Randomely \ selected \ transformers \ of \ swells - Mean \ number \ of \ swells }{Standard \ deviation \ of \ sweels}\\\\ Z_s_c_o_r_e= \dfrac{100-184}{25}\\\\ Z_s_c_o_r_e= \dfrac{-84}{25}\\\\ Z_s_c_o_r_e= -3.36[/tex]
Hence, The z-score for the number of sags for this transformer is 1.57 and the z-score for the number of swells for this transformer is -3.36.
For more details refer to the link given below.
https://brainly.com/question/15776766
