the heights of 18 year - old men are approximately normally distributed, with a mean 68 inches and a…

Explanation:

Step1: Calculate the z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 67$, $z_1=\frac{67 - 68}{3}=\frac{-1}{3}\approx - 0.33$. For $x = 69$, $z_2=\frac{69 - 68}{3}=\frac{1}{3}\approx0.33$.

Step2: Use the standard normal distribution table

We want to find $P(-0.33<Z<0.33)$. Since the standard - normal distribution is symmetric about $z = 0$, $P(-0.33<Z<0.33)=\Phi(0.33)-\Phi(-0.33)$. From the standard normal distribution table, $\Phi(0.33) = 0.6293$ and $\Phi(-0.33)=1 - 0.6293 = 0.3707$. So $P(-0.33<Z<0.33)=0.6293-(1 - 0.6293)=0.6293 - 0.3707=0.2586$.

Answer:

$0.2586$