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

90.66% of students scored below sofia

Answer 2

Answer: About 90.66% of students scored below Sofia.

Explanation:

Given : The scores on a standardized test are normally distributed with
`\mu=500` and
`\sigma=100`

Using the formula for z-value :

`z=(x-\mu)/(\sigma)`

Z-score for x= 632 will be :-

`z=(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*100=90.66\%`

Hence, about 90.66% of students scored below Sofia.