For Negative Binomial with p = 0.3 and r = 2, \(\mu = \frac{2}{0.3} = \frac{20}{3}\) and \(\sigma^2 = 2 \frac{0.7}{0.3^2} = \frac{140}{9}\) and so \(\sigma \approx 3.9\text{.}\) Therefore,
\begin{align*}
P(\mu - 2\sigma \le X \le \mu + 2\sigma) & = P(6.7 - 7.8 \le X \le 6.7 + 7.8)\\
& P( X \in \{2, 3, ... , 14, 15, 16 \} )
\end{align*}
Then,
\begin{equation*}
F(16) \approx 0.973888
\end{equation*}