However, using the Chebyshev’s Theorem,
\begin{equation*}
P( \mu - 1.8 \sigma \le X \le \mu + 1.8 \sigma) = P( \big | X - \mu \big | \lt 1.8 \cdot \sigma ) \gt 1 - \frac{1}{{1.8}^2} \approx 0.691.
\end{equation*}
The difference in these two results is not a problem since the first is designed to give you a precise answer with the knowledge that X itself has a known probability function whereas in the second case you only presume that X has the desired mean and standard deviation. With less information, you get a less precise lower bound but since the lower bound \(= 0.691 < 0.939 = \) exact value, then there is no conflict.