Question

The distribution of heights of women for a certain country is approximately​ Normal, with a mean of 63.6 inches and a standard deviation of 2.8 inches. How tall are the shortest 15​% of all women in this​ country?

Answer 1

Answer: 66.50 inches

Explanation:

Given : The distribution of heights of women for a certain country is approximately​ Normal with ,

`\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}`

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
`z=(x-\mu)/(\sigma)`

`1.0364=(x-63.6)/(2.8)\\\\\Rightarrow\ x=2.8*1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50`

Hence, the height of the shortest 15​% of all women in this​ country =66.50 inches.