#### Answer

The model underestimates the percentage of Americans by $1.9\%$.

#### Work Step by Step

The mathematical model:
$$P = -0.5x^{2} + 0.1x + 26.9$$
describes the percentage of Americans, $P$, in age group $x$ who had contact with a police officer.
Based on the graph, age group 20-29 is classified as Group 2; therefore, in this case, $x=2$.
Substituting this to the equation:
$$P = -0.5x^{2} + 0.1x + 26.9$$ $$P = -0.5(2)^{2} + 0.1(2) + 26.9$$ $$P = -0.5(4) + 0.2 + 26.9$$ $$P = -2 + 0.2 + 26.9$$ $$P = 25.1\%$$
The graph shows that $27\%$ of Americans in age group 20-29 had contact with a police officer. Therefore, the model underestimates the percentage of Americans by:
$$27-25.1=1.9\%$$