Question

the scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100. sofia scored 632 on the test. what percent of students scored below sofia?

Answer 1

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 :-

$P(z$

In percent, $0.9066\times100=90.66\%$

Hence, about 90.66%  of students scored below Sofia.

Answer 2

90.66% of students scored below sofia