5.2. The Density Curve of the Normal Distribution http://www.ck12.org
It appears that the mean is about 0.5 and the inflection points are 0.45 and 0.55 respectively. This would lead to an
estimate of about 0.05 for the standard deviation.
The actual statistics for this distribution are:
s≈ 0. 04988
x ̄≈ 0. 04997We can verify this using expectations from the empirical rule. In the following graph, we have highlighted the bins
that are contained within one standard deviation of the mean.
If you estimate the relative frequencies from each bin, they total remarkably close to 68%!
Calculating Density Curve Areas
While it is convenient to estimate areas using the empirical rule, we need more precise methods to calculate the areas
for other values. In Calculus you study methods for calculating the area under a curve, but in statistics, we are not
so concerned about the specific method used to calculate these areas. We will use formulas or technology to do the
calculations for us.