Continuity Correction in the Normal Approximation

Let $S \sim \mathrm{Bin}(200, 0.45)$. Use the CLT with a continuity correction to approximate $P(S = 85)$.

Recall that for a discrete integer-valued random variable, $P(S = k) \approx \Phi\!\left(\frac{k + 0.5 - \mu}{\sigma}\right) - \Phi\!\left(\frac{k - 0.5 - \mu}{\sigma}\right)$.

You may use: $\Phi(-0.64) \approx 0.2611$, $\Phi(-0.78) \approx 0.2177$.