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Relative Position of a Woman's Height to a Man

APSTAT-LISKNH

The height of an adult male is approximately normally distributed, with a mean of $69$ inches and a standard deviation of $2.8$ inches. The height of an adult female is approximately normally distributed, with a mean of $63.6$ inches and standard deviation $2.5$ inches.

What would be the approximate height of an adult female with the same standardized score ($z$-score) as an adult male with a height of $70.4$ inches?

A

$51.1$ inches

B

$62.4$ inches

C

$64.9$ inches

D

$70.4$ inches

E

$76.1$ inches