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?

easternerjx
2022-09-25
Answered

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Matthias Calhoun

Answered 2022-09-26
Author has **11** answers

From the given information,

$\mu =80\phantom{\rule{0ex}{0ex}}\sigma =15$

Consider, the percentile rank of a score of 84,

$P(X\le 84)=P(\frac{X-\mu}{\sigma}\le \frac{84-\mu}{\sigma})\phantom{\rule{0ex}{0ex}}=P(z\le \frac{84-80}{15})\phantom{\rule{0ex}{0ex}}=P(z\le 0.2667)\phantom{\rule{0ex}{0ex}}=0.605\phantom{\rule{0ex}{0ex}}\approx 61\mathrm{\%}$

Thus, the percentile value of 84 is 61%.

The percentile rank of 84 is 61.

$\mu =80\phantom{\rule{0ex}{0ex}}\sigma =15$

Consider, the percentile rank of a score of 84,

$P(X\le 84)=P(\frac{X-\mu}{\sigma}\le \frac{84-\mu}{\sigma})\phantom{\rule{0ex}{0ex}}=P(z\le \frac{84-80}{15})\phantom{\rule{0ex}{0ex}}=P(z\le 0.2667)\phantom{\rule{0ex}{0ex}}=0.605\phantom{\rule{0ex}{0ex}}\approx 61\mathrm{\%}$

Thus, the percentile value of 84 is 61%.

The percentile rank of 84 is 61.

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