Question

Imagine that in the future a college decides to change its admission standard to require an ACT score of 30. If the ACT was normally distributed with a mean of 26 and a standard deviation of 4, approximately what percentage of the population would be accepted for admission? 16% 32% 68% 84%

Answer 1

Given that

The data (Act score obtained by students) is Normally distributed

Mean of the given population

Standard deviation of the population

Here given that the ACT Score for admission (X)=30

Now lets find out the z score for this respective ACT score

now as we will see the bell shape curve of the distributed diagrame we find that for the % of student selected will be the student who comes under the area cover by respective value of probablity for this z score in the bell shape curve

so for getting the area covered by the probablity of the respective Z score we have to go through the table of normal probablity distribution .and from the table we get the respective value of area cover by p=0.84

so the % of student Accepted for the admiion =0.84*100=84%