Question

Height of Australian women is normally distributed with a mean of 172 cm and a standard deviation of 8 cm. The 5% tallest Australian women would have a height at least ___ cm

Answer 1

$Mean, \mu = 172$

$Standard\ Deviation, \sigma = 8$

The top $5\%$ are the individuals in the region $\alpha=0.05$ in a right tail probability distribution.

The corresponding $Z-value = 1.645$

$$Z= \frac{x-\mu}{\sigma}$$

Therefore

$$x= Z*\sigma +\mu$$

$$= 1.645*8+172=185.16$$

The tallest $5\%$ are at least $185.16\ cm$