Question

The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 700 and a standard deviation of 180. If a college requires a minimum score of 1100 for admission, what percentage of student do not satisfy that requirement?

answer: %

Answer 1

This question can be solved using the normal distribution method andc z value table.

Given : mean scores of students(U) = 700

Standard deviation of the scores( S) = 180

Minimum requirement of the score (X) = 1100

To find : Percentage of students who do not satisfy the requirement

We need to find z score corresponding to these scores, and then with the help of z table we can easily calculate the p value and from p value we can calculate the required %.

Z = (X - U) ÷ S

Z = (1100 - 700) ÷ 180

Z = 400 ÷ 180 = 2.22

P value for Z( 2.22) = 0.9868

It means 0.9868 fraction of students scored below 1100.

So , 0.9868×100 = 98.68 %

ANSWER. So , 98.68 % of students do not meet the requirement for the admission.