SL 4.9—Normal distribution

The normal distribution is symmetric about $x=\mu$, has mean = median = mode, and the curve is asymptotic to the x-axis, never touching it.

The total area under any normal curve is always exactly 1, regardless of $\sigma$.

Option B correctly states symmetry about $\mu$ and the asymptotic tails.

This describes tails touching the axis, which is the classic sketching error - tails only approach the axis asymptotically.

In a normal distribution mean, median and mode are all equal, not just mode differing from mean.

The total area is always 1 regardless of $\sigma$, since it represents total probability.

$156=162-6=\mu -\sigma$ and $168=162+6=\mu +\sigma$.

The range $\mu \pm 1\sigma$ corresponds to approximately 68% of the data.

So approximately 68% of women have heights between 156 cm and 168 cm.

95% corresponds to $\mu \pm 2\sigma$, i.e. 150 cm to 174 cm, not this range.

99.7% corresponds to $\mu \pm 3\sigma$, a much wider range.

50% would be a misunderstanding treating the distribution as uniform, ignoring the empirical rule.