Chirality of carbon atoms was assessed for each provided compound. A carbon atom is chiral if it is bonded to four distinct substituents. The analysis for such carbons is as follows:
$\text{CH}_3 - \text{CH}_2 - \text{CH(NO}_2\text{) - COOH}$ The third carbon atom ($\text{CH}$) is substituted with $-\text{CH}_3$, $-\text{CH}_2\text{COOH}$, $-\text{NO}_2$, and $-\text{H}$. This carbon atom is a chiral center.
$\text{CH}_3 - \text{CH}_2 - \text{CHBr - CH}_2 - \text{CH}_3$ The third carbon atom ($\text{CHBr}$) is substituted with $-\text{CH}_2\text{CH}_3$, $-\text{Br}$, $-\text{CH}_2\text{CH}_3$, and $-\text{H}$. Due to symmetry, this carbon atom is not chiral.
$\text{CH}_3 - \text{CH(I) - CH}_2 - \text{NO}_2$ The second carbon atom ($\text{CH(I)}$) is substituted with $-\text{CH}_3$, $-\text{CH}_2\text{NO}_2$, $-\text{I}$, and $-\text{H}$. This carbon atom is a chiral center.
$\text{CH}_3 - \text{CH}_2 - \text{CH(OH) - CH}_2\text{OH}$ The third carbon atom ($\text{CH(OH)}$) is substituted with $-\text{CH}_2\text{OH}$, $-\text{OH}$, $-\text{CH}_2\text{CH}_3$, and $-\text{H}$. This carbon atom is a chiral center.
The total count of compounds containing chiral carbon atoms is 3.