Answer to Question #154448 in Statistics and Probability for Tarrah

Question #154448

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


1
Expert's answer
2021-01-10T17:26:50-0500

Mean,μ=172Mean, \mu = 172

Standard Deviation,σ=8Standard\ Deviation, \sigma = 8


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


The corresponding Zvalue=1.645Z-value = 1.645



Z=xμσZ= \frac{x-\mu}{\sigma}

Therefore


x=Zσ+μx= Z*\sigma +\mu

=1.6458+172=185.16= 1.645*8+172=185.16

The tallest 5%5\% are at least 185.16 cm185.16\ cm


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