Finding percentage with mean and standard deviation

Question

Adult woman in china have heights which are normally distributed with the mean of 155cm and standard deviation of 8cm. Adult women in Japan have heights which are normally distrusted with mean of 158cm and standard deviation 6cm. Which country has a higher percentage of women taller than 167cm.

Answer 1

First, compute the z-scores for both countries.

 

 

z (China) = (167 - 155) / 8 = 1.5

 

z (Japan) = (167 - 158) / 6 = 1.5

 

 

The percentage greater than 167 cm depends on  the z-score.  Since they are the same, the percentage of women over 167 cm in height is the same.