Solution:
Given:
The data for men is as follows:
[tex]\begin{gathered} x=65 \\ \mu=70 \\ \sigma=4 \end{gathered}[/tex]
To get the percent of men that are shorter than 65 inches, we find the Z-scores.
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{65-70}{4} \\ Z=\frac{-5}{4} \\ Z=-1.25 \end{gathered}[/tex]
From the Z-scores table,
[tex]\begin{gathered} P(x<-1.25)=0.10565 \\ \\ As\text{ a percent,} \\ P(x<-1.25)=0.10565\times100\text{ \%} \\ P(x<-1.25)=10.565\text{ \%} \\ \\ To\text{ 2 decimal places,} \\ P(x<-1.25)=10.57\text{ \%} \end{gathered}[/tex]
Therefore, the percentage of men that are shorter than 65 inches to 2 decimal places is 10.57%
