Answer
See below
Work Step by Step
$\text{z-score}=\frac{\text{data item-mean}}{\text{standard deviation}}$
Hence here the z-score is: $z_{65}=\frac{65-69}{2.75}=-1.5\\z_{75}=\frac{75-69}{2.75}=2.2$
Then, using the table: $P(-1.2\leq z\geq 2.2)=0.9861-0.0668=0.9193$
The probability that 5 randomly selected men all have heights between 65 inches and 75 inches is $(0.9193)^3=0.65578$
