Answer: About 90.66% of students scored below Sofia.
Step-by-step explanation:
Given : The scores on a standardized test are normally distributed with [tex]\mu=500[/tex] and [tex]\sigma=100[/tex]
Using the formula for z-value :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Z-score for x= 632 will be :-
[tex]z=\dfrac{632-500}{100}=1.32[/tex]
Using standard normal distribution table for z, the probbaillity that the students scored below Sofia will be :-
[tex]P(z<1.32)=0.9065825\approx0.9066[/tex]
In percent, [tex]0.9066\times100=90.66\%[/tex]
Hence, about 90.66% of students scored below Sofia.
