Question

*You will use the following scenario forquestions 5-8*The mean height of adult men is 70inches with a standard deviation of 4while the mean height of adult womenis 65 inches with a standard deviationof 3.5.What percent of men are shorter than65 inches?*Write your answer as a percent andround to 2 decimal places*

Answer 1

Given:

The data for men is as follows:

`\begin{gathered} x=65 \\ \mu=70 \\ \sigma=4 \end{gathered}`

To get the percent of men that are shorter than 65 inches, we find the Z-scores.

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ Z=(65-70)/(4) \\ Z=(-5)/(4) \\ Z=-1.25 \end{gathered}`

From the Z-scores table,

`\begin{gathered} P(x<-1.25)=0.10565 \\ \\ As\text{ a percent,} \\ P(x<-1.25)=0.10565*100\text{ \%} \\ P(x<-1.25)=10.565\text{ \%} \\ \\ To\text{ 2 decimal places,} \\ P(x<-1.25)=10.57\text{ \%} \end{gathered}`

Therefore, the percentage of men that are shorter than 65 inches to 2 decimal places is 10.57%