5.2. The Density Curve of the Normal Distribution http://www.ck12.org
Notice that the curves are spread increasingly wider. Lines have been drawn to show the points one standard
deviation on either side of the mean. Look atwherethis happens on each density curve. Here is a normal distribution
with an even larger standard deviation.
Could you predict the standard deviation of this distribution from estimating the point on the density curve?
You may notice that the density curve changes shape at this point in each of our examples. In Calculus, we learn
to call this shape changing location aninflection point. It is the point where the curve changesconcavity. Starting
from the mean and heading outward to the left and right, the curve is concave down (it looks like a mountain, or
shape). After passing this point, the curve is concave up (it looks like a valley or shape). We will leave it to the
Calculus students to prove it, but in a normal density curve, this inflection point is always exactly one standard
deviation away from the mean.