The normal distribution appears often in population and natural distributions.
It is often referred to as the bell curve.
Normal distributions are assumed to be perfectly symmetric.

Note: this is not always the case in practice, but it is an accurate approximation.

A key characteristic of the normal distribution is that the mean and median are equal and correspond to the highest frequency

Note: as a result of this, either the mean or median can be used to measure the centre of the distribution.

The standard deviation is the appropriate measure of spread for a normal distribution.

The 68-95-99.7% Rule

A convenient characteristic of the normal distribution is that 68% of datapoint lie within one standard deviation of the centre (i.e. between the x-values of $\bar{x}-s$ and $\bar{x}+s$ ), 95% lie within 2 standard deviations of the centre, and 99.7% lie within 3 standard deviations of the centre.

Example: applying the 68-95-99.7% Rule

Assume the height of a group of people was measured and found to be normally distributed with a mean of 1.5m and standard deviation of 0.1m. The following normal distribution shows this model:

If we wanted to find the percentage of people with heights between 1.3m and 1.6m, we could do so by summing the percentage values of the encompassed regions (shaded below):

Thus, the percentage of people with heights between 1.3m and 1.6m is:

$13.5+34+34=81.5 \%$

Previous Topic

Back to Lesson

Next Topic