Where the normal distribution function changes curvature

What is a point of inflection? Find the point of inflection of the cumulative distribution function of a normal random variable with mean $\mu$ and standard deviation $\sigma$.

At $x=\mu$. An inflection point is where the second derivative changes sign, so the curve switches between convex and concave. The CDF's second derivative is the derivative of the density, which is positive for $x<\mu$ and negative for $x>\mu$; the CDF is convex then concave. (The density itself inflects at $\mu\pm\sigma$.)