Answer:
(a) -3.708
(b) 1.706
(c) 0.490
Step-by-step explanation:
The z-score of normal distribution is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
(a)
Given:
Score is, [tex]x=268[/tex]
Mean value is, [tex]\mu =425[/tex]
Standard deviation is, [tex]\sigma = 51[/tex]
z-score is, [tex]z=\frac{268-425}{51}=\frac{-157}{51}=-3.078[/tex]
(b)
Given:
Score is, [tex]x=512[/tex]
Mean value is, [tex]\mu =425[/tex]
Standard deviation is, [tex]\sigma = 51[/tex]
z-score is, [tex]z=\frac{512-425}{51}=\frac{87}{51}=1.706[/tex]
(c)
Given:
Score is, [tex]x=450[/tex]
Mean value is, [tex]\mu =425[/tex]
Standard deviation is, [tex]\sigma = 51[/tex]
z-score is, [tex]z=\frac{450-425}{51}=\frac{25}{51}=0.490[/tex]
