# A class of 135 students took a final examination in mathematics. The scores were normally distributed with a mean score of 68% and a standard deviation of 8.5%. Determine the percentile rank of each of the following people: (a) Jennifer, who scored 78 % (b) Steven, who got 55 % (c) Jessica, who was very happy with her mark of 89 %

A class of 135 students took a final examination in mathematics. The scores were normally distributed with a mean score of 68% and a standard deviation of 8.5%. Determine the percentile rank of each of the following people:
(a) Jennifer, who scored 78 %
(b) Steven, who got 55 %
(c) Jessica, who was very happy with her mark of 89 %
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Osvaldo Crosby
Given :
n = 135
$\text{Mean}=\mu =68$
$\text{Standard deviation}=\sigma =8.5$
a) $Z=\frac{X-\mu }{\sigma }=\frac{78-68}{8.5}=1.18$
P(Z < 1.18) = 0.8810 (from standard normal table)
Percentile rank = 88.10%
b) $Z=\frac{55-68}{8.5}=1.53\phantom{\rule{0ex}{0ex}}P\left(Z<-1.53\right)=0.0630\phantom{\rule{0ex}{0ex}}⇒\text{Percentile rank}=6.3\mathrm{%}$
c) $Z=\frac{89-68}{8.5}=2.47\phantom{\rule{0ex}{0ex}}P\left(Z<2.47\right)=0.9932\phantom{\rule{0ex}{0ex}}⇒\text{Percentile rank}=99.32\mathrm{%}$