Question

If the heights of a population of men are approximately Normally distributed, and the middle $99.7\%$have heights between $5\prime 0″$and $7\prime 0″$what is the standard deviation of the heights in this population?

$$\begin{gathered} a.1″ \\ b.3″ \\ c.4″ \\ d.6″ \\ e.12″ \end{gathered}$$

Short answer

The correct option is c. $4″$

Step-by-step solution

Given information

$99.7\%$of the height is between $5’0’’$and$7’0’’$

Calculation

The normal distribution rule states that $99.7\%$ of data will fall within three standard deviations of the mean.

The mean is $6\text{'}0"$ since it is at the midpoint of the interval.

Also, 3 standard deviation is between $5\text{'}0"$ and $6\text{'}0"$ tall.

$3\sigma =1\text{'}0\text{'}\text{'}=12\text{'}\text{'}$

Dividing each side by 3:

$\sigma =\frac{12\text{'}}{4}=4\text{'}\text{'}$