Question

3. What percent of young women have heights between 62 and 72 inches? Show your work.

Short answer

The percentage young women have heights between 62 and 72 inches are$84\%.$

Step-by-step solution

Given Information

Heights of young women aged between$=18to24.$

Percentage of young women with heights greater than 67 inches$=?$

Explanation 

Given that,

$\mu =64.5$

$\sigma =2.5$

$$\begin{gathered} P(62<x<72)=P\left(\frac{62-64.5}{2.5}<\frac{x-\mu }{\sigma }<\frac{72-64.5}{2.5}\right) \\ =P\left(\frac{-2.5}{2.5}<z<\frac{7.5}{2.5}\right) \\ =P(-1<z<3) \\ =P(z<3)-P(z<-1) \end{gathered}$$

Substitute the given expression,

$$\begin{gathered} =0.9987-0.1587 \\ =0.84 \end{gathered}$$

We get,

$=84\%$.