Solution
\[
\begin{aligned}
& \text { Expectation } \mathrm{E}(\mathrm{x})=\sum \mathrm{x}_{\mathrm{i}} \mathrm{P}\left(\mathrm{x}_{\mathrm{i}}\right)=\frac{263}{15} \\
& \Rightarrow \frac{28 \times 2 \mathrm{k}+30 \mathrm{k}+64 \mathrm{k}+102 \mathrm{k}+36 \mathrm{k}+76 \mathrm{k}+120 \mathrm{k}+42 \mathrm{k}}{7 \times 15}=\frac{263}{15} \\
& \Rightarrow 526 \mathrm{k}=263 \times 7 \Rightarrow \mathrm{k}=\frac{7}{2}
\end{aligned}
\]
[t]{|l|l|l|l|l|l|l|l|l|}
X |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
| P(x) |
$\frac{2}{15}$ |
$\frac{1}{15}$ |
$\frac{2}{15}$ |
$\frac{3}{15}$ |
$\frac{1}{15}$ |
$\frac{2}{15}$ |
$\frac{3}{15}$ |
$\frac{1}{15}$ |
\[
P(x<20)=\frac{2+1+2+3+1+2}{15}=\frac{11}{15} \text { Answer }(3)
\]
.
