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The population of the heights for a species of adult male gorillas are approximately normally distributed with a mean height of $72\text{ inches}$ and a standard deviation of $3.1\text{ inches}$. The population of the heights for the same species of adult female gorillas are approximately normally distributed with an average height of $63\text{ inches}$ and a standard deviation of $2.6\text{ inches}$.

What height must a female gorilla have in order to have the same standardized height ($z$-score) as the $66\text{ inch}$ male gorilla?

What percentile will these gorillas’ heights be for their respective genders?

A

$57.0\text{ inches}, 1.05\%$

B

$57.96\text{ inches}, 2.65\%$

C

$57.96\text{ inches}, 97.35\%$

D

$68.04\text{ inches}, 2.65\%$

E

$68.04\text{ inches}, 97.35\%$

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