Q.Which of the following is not true regarding the normal distribution ?

Checking each statement against the normal distribution's known properties shows the maximum-height claim is false in general — the correct maximum height is $1/(\sigma\sqrt{2\pi})$, not $1/\sqrt{2\pi}$.

1. The normal distribution's pdf is $f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}$.
2. Statement (a): the points of inflection occur where $f''(x)=0$, which for the normal curve are exactly at $x=\mu\pm\sigma$ — this is a true, standard property.
3. Statement (b): the normal distribution is symmetric about $\mu$, so its skewness is $0$ — true. …