In details

Normal distribution

Normal distribution is the most important statistical distribution, considering the practical and theoretical question.

We have already seen that this type of distribution is bell-shaped, unimodal, symmetrical in relation to its mean.

Considering the probability of occurrence, the area under its curve is 100%. This means that the probability of an observation assuming a value between any two points is equal to the area between these two points.

68.26% => 1 deviation
95.44% => 2 deviations
99.73% => 3 deviations
In the figure above, there are brown bars representing standard deviations. The further from the center of the normal curve, the more area below the curve there will be. At a standard deviation, we have 68.26% of the observations contained. At two standard deviations we have 95.44% of the comprehended data and finally at three deviations we have 99.73%. We can conclude that the greater the variability of data relative to the mean, the more likely we are to find the value we are looking for below normal.

Property 1

f (x) is symmetrical about the origin, x = mean = 0.

Property 2

f (x) has a maximum for z = 0, in which case its ordinate is 0.39.


f (x) tends to zero when x tends to + infinity or - infinity.

Property 4

f (x) has two inflection points whose abscissa is worth + SD and mean - SD, or when z has two inflection points whose abscissa is worth +1 and -1.

To obtain the probability under the normal curve, we use the central range table.

Click here to see example 8

Next: Exercises