Answer: 66.50 inches
Step-by-step explanation:
Given : The distribution of heights of women for a certain country is approximately Normal with ,
[tex]\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}[/tex]
To find the height of the shortest 15% of all women, first we need to find the z-score corresponding to the p-value 0.15 from the standard normal distribution table, we get 1.0364.
Let x be the random variable that represents the height of the randomly selected woman.
Then[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]1.0364=\dfrac{x-63.6}{2.8}\\\\\Rightarrow\ x=2.8\times1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50[/tex]
Hence, the height of the shortest 15% of all women in this country =66.50 inches.
