(19) (This question is worth 12 points) In response to the national strategy of "targeted poverty alleviation and industrial support," Harbin City is recruiting volunteer advocates for the "Poverty Alleviation Policy" from the public. From 500 volunteers aged between $[20,45]$, 100 are randomly selected, and their age frequency distribution histogram is shown in the figure.
(1) Find the value of $x$ in the figure;
(2) From the 100 selected volunteers, 10 are chosen using stratified sampling based on age to participate in the central square publicity campaign. Then, 3 of these 10 volunteers are selected to serve as primary leaders. Let the number of these 3 volunteers who are "under 35 years old" be $X$. Find the distribution of $X$ and its expected value.
19. (1) According to the frequency distribution histogram, we have $(0.01+0.02+0.04+x+0.07) \times 5=1$, solving for $x$ gives $x=0.06 \ldots \ldots \ldots .2$ points
(2) Using stratified sampling, 10 volunteers are selected from 100, of which 6 are "under 35 years old" and 4 are "35 years old or older", ................... 4 points. Therefore, the possible values of $X$ are $0,1,2,3$.
$P(X=0)=\frac{C_{4}^{3}}{C_{10}^{3}}=\frac{1}{30}, \quad P(X=1)=\frac{C_{6}^{1} C_{4}^{2}}{C_{10}^{3}}=\frac{3}{10}, \quad P(X=2)=\frac{C_{6}^{2} C_{4}^{1}}{C_{10}^{3}}=\frac{1}{2}, \quad P(X=3)=\frac{C_{6}^{3}}{C_{10}^{3}}=\frac{1}{6}$. Thus, the distribution of $X$ is
\begin{tabular}{|l|l|l|l|l|}
\hline$Y$ & 0 & 1 & 2 & 3 \\
\hline$P$ & $\frac{1}{30}$ & $\frac{3}{10}$ & $\frac{1}{2}$ & $\frac{1}{6}$ \\
\hline
\end{tabular}
$$
E(Y)=0 \times \frac{1}{30}+1 \times \frac{3}{10}+2 \times \frac{1}{2}+3 \times \frac{1}{6}=1.8
$$
10 points