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