Question

A school requires an entrance exam score that is in the top 3% of the population in order to be accepted.

If an entrance exam has a mean of 500 and a standard deviation of 55, what is the minimum qualifying score to be accepted at the school?

Answer Choices:
A.) 397
B.) 349
C.) 603
D.) 651

PLEASE SHOW YOUR WORK TOO. I really don't understand. Also, how do you read z-score chart.

Answer 1

a. 485 is %3 of 500, but the deviation sets it slightly lower than that

Answer 2

First, we assume the distribution is normal, since it is not given in the question.

Next, get a Z-table, such as
stat.ufl.edu/~athienit/Tables/Ztable.pdf
and look through the table for 97% shaded.
The corresponding Z-value should be 1.88 SD (standard deviations) for 96.99%.
Now since
Z=(X-mean)/SD
where
mean=500, SD=55
Solve for X.