Respuesta :
Answer:
(a) -1.0133
(b) 2.32
(c) -2
(d) 0.9867
(e) 2.9867
Step-by-step explanation:
The z-score of a raw score X is a standardized score that follows a normal distribution with mean 0 and standard deviation 1.
The formula to compute the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given:
Mean (μ) = $775
Standard deviation (σ) = $75
(a)
For X = $699 the z-score is:
[tex]z=\frac{x-\mu}{\sigma}\\=\frac{699-775}{75} \\=-1.0133[/tex]
(b)
For X = $949 the z-score is:
[tex]z=\frac{x-\mu}{\sigma}\\=\frac{949-775}{75} \\=2.32[/tex]
(c)
For X = $625 the z-score is:
[tex]z=\frac{x-\mu}{\sigma}\\=\frac{625-775}{75} \\=-2[/tex]
(d)
For X = $849 the z-score is:
[tex]z=\frac{x-\mu}{\sigma}\\=\frac{849-775}{75} \\=0.9867[/tex]
(e)
For X = $999 the z-score is:
[tex]z=\frac{x-\mu}{\sigma}\\=\frac{999-775}{75} \\=2.9867[/tex]
Answer:
a) -1.013
b) 2.32
c) -2
d) 0.9867
e) 2.9867
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $775
Standard Deviation, σ = $75
We are given that the distribution of average price of a laptop is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find z-score for corresponding
a. $699
[tex]z = \displaystyle\frac{699 - 775}{75} = -1.013[/tex]
b. $949
[tex]z = \displaystyle\frac{949 - 775}{75} = 2.32[/tex]
c. $625
[tex]z = \displaystyle\frac{625 - 775}{75} = -2[/tex]
d. $849
[tex]z = \displaystyle\frac{849 - 775}{75} = 0.9867[/tex]
e. $999
[tex]z = \displaystyle\frac{999 - 775}{75} = 2.9867[/tex]
