$A$ random variable $X$ has the following probability distribution. Find the value of $k$ and the value of $P(3 < X \leq 6)$.
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(x)$ $k$ $2k$ $3k$ $4k$ $4k$ $3k$ $2k$ $k$ $k$
| $X = x$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|---|
| $P(x)$ | $k$ | $2k$ | $3k$ | $4k$ | $4k$ | $3k$ | $2k$ | $k$ | $k$ |
- A$\frac{1}{20}, \frac{3}{7}$
- B$\frac{5}{21}, \frac{3}{7}$
- C$\frac{1}{21}, \frac{3}{7}$
- D$\frac{1}{20}, \frac{4}{7}$
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