Question

The result of nationwide aptitude test in mathematics are normally distributed with m=80 and s= 15 what is the percentile rank of a score of 84

Answer 1

$\mu=80\\\sigma=15$

We first determine, $p(x\le 84)=p({x-\mu\over \sigma}\le{84-\mu\over \sigma})=p(Z\le {84-80\over 15})=p(Z\le0.27)=0.6064$

The percentile rank is, $0.6064\times100\%=60.64\%$

Therefore, with score, $x=84$, the percentile rank is 60.64 %