5.2. The Density Curve of the Normal Distribution http://www.ck12.org
However, the advantage of using the calculator is that it is unnecessary to standardize. We can simply enter the
mean and standard deviation from the original population distribution of candy, avoiding thez−score calculation
completely.
Lesson Summary
Adensity curveis an idealized representation of a distribution in which the area under the curve is defined as 1, or in
terms of percentages, 100% of the data. Anormal density curveis simply a density curve for a normal distribution.
Normal density curves have twoinflection points, which are the points on the curve where it changes concavity.
Remarkably, these points correspond to the points in the normal distribution that are exactly 1 standard deviation
away from the mean. Applying the empirical rule tells us that the area under the normal density curve between these
two points is approximately 0.68. This is most commonly thought of in terms of probability, e.g. the probability
of choosing a value at random from this distribution and having it be within 1 standard deviation of the mean is
0 .68. Calculating other areas under the curve can be done using az−tableor using thenormalcdfcommand on the
TI-83/84. Thez−table provides the area less than a particularz−score for the standard normal density curve. The
calculator command allows you to specify two values, either standardized or not, and will calculate the area between
those values.