Finding variance from bell curve

Question

Find variance from the graph given. I know the mean is 6 but I have no idea how to find the variance using this graph

Answer 1

Let $f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{-\frac{(x-6)^2}{2\sigma^2} }$ be the pdf. From the graph we see that $f(6) = \frac{1}{\sigma \sqrt{2\pi} } \approx .08$, and you can use that equation to solve for $\sigma^2.$

Answer 2

$\mu\pm\sigma$ are the inflection points: the points where the graph stops getting steeper and starts getting less steep.