12. In a provincial science popularization knowledge competition, the preliminary scores of 3000 participants from a city are statistically shown in the figure below.
(1) Find the value of $t$, and estimate the number of participants in the city whose scores fall in the range $[80,90)$ in this competition;
(2) If the city plans to select 1500 participants to advance to the final, how should the qualifying score for the final be set?
(3) If the scores of the city's participants are used to estimate the scores of the provincial participants, and now 4 participants are randomly selected from the provincial participants, let the number of participants with scores of 80 (including 80) or above be $\xi$, find the distribution and expectation of $\xi$.
(1) $(2 t+3 t+6 t+7 t+2 t) \times 10=1 \Rightarrow t=\frac{1}{200}$. Since the frequency of scores in the range $[80,90)$ is 0.3, the corresponding number of participants is $3000 \times 0.3=900$.
(2) The frequency corresponding to 1500 people is 0.5, so the score $x$ should be the median of all scores. Since $\frac{2+3+7}{20}=0.6$, we have $\frac{80-70}{0.35}=\frac{x-70}{0.25} \Rightarrow x-70=\frac{50}{7} \Rightarrow x \approx 77.14$.
(3) The frequency of scores 80 (including 80) and above is 0.4, so $P(\xi=i)=C_{4}^{i} 0.6^{4-i} 0.4^{i}(i=0,1,2,3,4)$. The distribution table is as follows:
\begin{tabular}{|c|c|c|c|c|c|}
\hline$\xi$ & 0 & 1 & 2 & 3 & 4 \\
\hline$P$ & $\frac{81}{625}$ & $\frac{216}{625}$ & $\frac{216}{625}$ & $\frac{96}{625}$ & $\frac{16}{625}$ \\
\hline
\end{tabular}
The expectation of $\xi$ is $E \xi=4 \times 0.4=1.6$.