# NCAE shows that the average score of the students is 80 and sd is 15. What is the percentile rank of a score of 84?

NCAE shows that the average score of the students is 80 and sd is 15. What is the percentile rank of a score of 84?
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Matthias Calhoun
From the given information,
$\mu =80\phantom{\rule{0ex}{0ex}}\sigma =15$
Consider, the percentile rank of a score of 84,
$P\left(X\le 84\right)=P\left(\frac{X-\mu }{\sigma }\le \frac{84-\mu }{\sigma }\right)\phantom{\rule{0ex}{0ex}}=P\left(z\le \frac{84-80}{15}\right)\phantom{\rule{0ex}{0ex}}=P\left(z\le 0.2667\right)\phantom{\rule{0ex}{0ex}}=0.605\phantom{\rule{0ex}{0ex}}\approx 61\mathrm{%}$
Thus, the percentile value of 84 is 61%.
The percentile rank of 84 is 61.