Answer: 0.8413
Step-by-step explanation:
Given : The average score on a standardized test is [tex]\mu=\text{750 points }[/tex]
Standard deviation : [tex]\sigma=50\text{ points}[/tex]
Let x be the score of randomly selected student.
The z-score for standardized test :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 700
[tex]z=\dfrac{700-750}{50}=-1[/tex]
The p-value = [tex]P(x>700)=P(z>-1)[/tex]
[tex]1-P(z<1)=1-0.1586553=0.8413447\approx0.8413[/tex]
Therefore, the probability that a student scores more than 700 on the standardized test = 0.8413
