Is height normally distributed?

Matthews [1] details John William 'Bud' Rogan (1860s - 1905) of Tennessee who was 2.67 metres tall. Given a mean of 1.70 m and a standard deviation of 0.07 m this makes him more than 13 standard deviations taller than his fellow American men of the time. Matthews argued that the normal distribution isn't appropriate for height because Mr Rogan was one man in 10 to the power of 44.

A contemporary of Mr Rogan was Charles Sherwood Stratton (1838 - 1883) who, at 0.64 m tall, was 15 standard deviations shorter than the mean.

These extremes would indicate that height is not normally distributed due to the tails of the normal distribution not being fat enough.

[1] R. Matthews, Chancing It: The Laws of Chance and How They Can Work for You, Profile Books, London, 2016.