Question

Most graduate business schools require applicants to take the gmat. scores on this test are approximately normally distributed with a mean of 545 points and a standard deviation of 100 points. what score do you need to be in the top 5% (approximately the scores needed for top schools)?

Answer 1

We are looking for the probability :
$P(X > n)=0.05$
Transform the law to standard normal like this:
$P(\dfrac{X-545}{100}> \dfrac{n-545}{100})=0.05$
The above formula is equivalent to this one:
$P(\dfrac{X-545}{100}< \dfrac{n-545}{100})=0.95$
From normal law table, we read the value of $\dfrac{X-545}{100}$.
$\dfrac{X-545}{100}=1.7$
Solving the above equation for the score n:
$X-545=170$
$X=715$, it is the score we are looking for.